Why are space shuttles always rockets, and take off straight upward?

So spaceplanes are a thing
https://en.wikipedia.org/wiki/Spaceplane

But they do take off vertically. From my experiemce with kerbal space program, it's because of the density of the atmosphere. The closer to sea level, the denser the atmosphere and the more drag from air resistance. So instead of burning a ton of fuel trying to get through the thick atmosphere, you go straight up until it's thinner and then you start to turn. Makes a huge difference.

There's also the fact that bigger rockets with more fuel create more drag so the solution isn't "just make it bigger"

You’re 12 right?

It’s mainly of “you need to go a lot faster than an airplane does”, which means the engines needed to go that fast need different fuel, and when you go high enough you don’t have enough air to burn the fuel with so you have to bring your own, which means your spaceship now gets bigger and heavier……which means bigger engines and more fuel and oxidizer.

And then the lift part…..air provides the lift, but there’s less air the higher you go, until you hit the point where you both don’t have enough air to hold you up AND you don’t have enough air to feed your engines.

So with that combination, with current technology, it’s only feasible to go up as fast as you can to get out of the atmosphere, then go sideways as fast as possible to get to orbital speed. Hence the current launch paths.

If they went down, it'd be a lot harder to get to space.

Planes rely on air to get lift. There is very little air in space.

There’s a number of assumptions we’ll have to correct first:

1. Airplanes are air planes. They stay up by moving fast enough over the air that it is collectively more dense, causing them to float. They fly up to 30,000 feet (they can go higher, but….)

The earth has an atmosphere. The further away from the surface you get, the less atmosphere, the faster the airplane has to fly to stay afloat.

Now we get to the next bit: how do planes propel themselves?

They do it by reacting fuel with heat and oxygen, via a propeller or jet turbine (which compresses the air providing a more dense oxygen source).

Again, what happens as you get further from the earth’s surface? You get less oxygen, meaning less propulsion so the plane goes slower for the same amount of fuel, until you hit the point where there’s either not enough air to provide lift, or there’s not enough oxygen to react with the fuel.

So the solution is to carry all your reactants with you. This usually involves liquid oxygen. That’s heavy and under pressure, so there’s a push to strip as much unnecessary weight as you can from the vessel so there’s room for something other than the fuel.

The easiest solution is to get rid of heavy wings, and stick to small fins that can assist in steering while there’s enough atmosphere around to push against.

Now we get to the next bit:

What’s the FASTEST way to get to space? The fastest way uses the least energy, and you’re having to carry your energy source with you.

The fastest way is to go almost straight away from the earth.

However, this isn’t the only solution, just the easiest.

Back when the X prize challenge was presented, a bunch of solutions to reusable spacecraft were tried. Balloons and blimps to raise the rocket as far into the atmosphere as possible before launch; airplanes that get to cruising altitude and then “drop” the rocket to go the rest of the way under their own power. This took more energy, but the first bit didn’t have to be self-contained.

But it turned out the winning solution that could escape earth’s gravity well was the Falcon 9. A multi-stage rocket with different fuels for different stages that used a rocket as a launch platform, and that rocket could return to base to be used again.

It's because the research can be used to make better missiles.

I'm only adding to the already well established answers here, but spacecraft also need to further away from the earth's gravity well which requires a huge amount of energy. If you're lifting 100 tons (if you're including some kind of aeroplane + spacecraft), we are talking at least something like 100+ gigajoules of energy to get it into space in the first place, excluding orbital velocity. So the immense energy capacity of rocket fuel tends to be the only one sufficient for this, plus as the fuel tanks empty and the drag decreases, the acceleration of the rocket dramatically increases.

A lot of this makes complete sense why rockets are the only viable solution for the time being.

There have been planes made to carry spacecraft to the upper atmosphere before launch.

https://en.wikipedia.org/wiki/Scaled_Composites_White_Knight

https://en.wikipedia.org/wiki/Scaled_Composites_White_Knight_Two

gravity well

The only caveat here is that anything in orbit is nowhere near escaping the gravity well. The earth is pulling on the International Space Station at about 90% of the force as at sea level. It's just that everything is going so fast it misses the ground.

From my experiemce with kerbal space program

Kerbal is awesome for introducing people to things like orbital mechanics.

Also want to point out that KSP doesn't fully model gravity, it is a simplified approach that works for most things you'd do in a game. For eample, an object can only be affected by a single gravity source at a time. So there are no lagrange points. Going from Kerbin to the Mun, your craft is affected by Kerbins gravity until you enter the Mun sphere of influence where it immediately shifts.

It's close enough for most stuff, but does have some fundamental issues like that when trying to model more than fairly basic launches and orbits.

Pretty good summary. I'll add a couple corrections:

This usually involves liquid oxygen. That’s heavy and under pressure

The critical point) of oxygen is below room temperature, meaning it is not possible to keep oxygen liquid using pressure alone. For rockets, liquid oxygen is typically loaded within hours or minutes prior to launch, before it has a chance to warm up and boil off.

winning solution that could escape earth’s gravity well was the Falcon 9. A multi-stage rocket with different fuels for different stages

Falcon 9 is a two-stage rocket, but it uses the same propellants (kerosene and liquid oxygen) on both stages.

Also, I'm not sure if I would call the Falcon 9 the winning solution, just the "winningest" solution so far. SpaceX's Starship, Stoke Space's Nova, and any of the upcoming Falcon 9 clones have the potential to improve on the Falcon 9 design or solve the challenge of reusability in slightly different ways.

Getting to space is easy. Getting to orbit is HARD.
To reach orbit, you don't need to just go further up.
You need to go really, really, really fast.

The fastest jet airplane flies up to 3500 km/h.
Orbital speed is 29800 km/h.

Every additional pound of weight on your craft needs to be accelerated to that speed, which requires fuel.
That additional fuel also needs to be accelerated, which requires more fuel.
So it's really important to keep your spacecraft light, because its take-off weight (including fuel) scales exponentially with its dry weight (the stuff you actually want to move).

And this is why spaceplanes are bad: They carry tons of wings and control surfaces, which are only useful during the first 10% of acceleration towards orbital speed, and useless weight throughout the entire mission afterwards.

We usually say "it's not rocket science" to mean something is not that hard. Well, this IS rocket science, and it IS that hard. You can explore the mechanics of these issues in a decent space simulator like Kerbal Space Program (1 is a bit janky but still the gold standard, 2 sucks and is abandonware), Juno: New Origins (I find the career mode contains a lot of nonsense distracting from actual rocketry) and Kitten Space Agency (free, superb simulation but pretty alpha/indev status, hardcore, and no handholding)

So, there are a few problems you're facing right out of the gate:

1. Rockets are HEAVY. The fuel is typically somewhere between 90 and 99% of the mass of the entire vehicle. It is functionally just a bunch of metal tubes and cavities full of fuel and a little bit of hardware and electronics to make it all work. The phenomenon known as the "tyranny of the rocket equation" is the cause of this. For every extra bit of distance you want to go, you need to propel not just the rocket itself that extra distance, but also enough fuel to propel that additional fuel that you will need. When up to 99% of your mass IS fuel, adding more distance means mostly you're just moving fuel, and that means it takes more fuel to move that fuel, and so on. It's fuel, fuel, and more fuel all the way down.
2. Rockets are inefficient. Chemical rockets are almost so inefficient that if they were even a little bit less efficient than they are, they would be theoretically incapable of escaping Earth's gravity and reaching orbit. You have very little margin to operate within. We have to use the very best, lightest, densest, and most powerful fuels because we really don't have a lot of wiggle room here. Earth's gravity is quite strong, and our atmosphere is quite thick, and our best chemical fuels available are only barely capable of the task that reaching orbit requires of them. That's the other part of why the rockets have to be 90%+ fuel, it's to satisfy the rocket's gluttonous inefficiency.
3. You need a rocket. Why do you need a rocket you ask? Well, technically, you might be able to do it without one, but it would an even more horrible experience and practically adds so many other issues, which we'll talk about later. You would have to do all your propulsion in the atmosphere (or even worse, on the ground) where that thrust is actually at its least efficient due to atmospheric resistance. You need a rocket because a rocket is the only type of propulsion that a) works in an atmosphere and b) works in a vacuum at the same time, and c) provides enough thrust to achieve a thrust-to-weight ratio of greater than 1 (in other words, can push the rocket upwards more strongly than the Earth's gravity can pull it back down) and d) actually gets more powerful and accelerates faster (same engine thrust is now pushing vastly less fuel) as you get out of the atmosphere at exactly when you most need it and it's working most efficiently for you. Propellers obviously do not work in vacuum. Jet engines also do not work in vacuum, because they cannot ignite and burn their fuel without oxygen (and oxygen is actually the heavier part of the rocket's fuel, so even if you develop a complex hybrid air-breathing jet/rocket engine, you don't gain much efficiency anyway). Ion/plasma engines do not have enough thrust to weight. Anything else is pretty much just a rocket with extra weight and complexity. So rockets it is.

What happens when you bring a jet up to higher and higher altitudes at higher and higher speeds? Well, it's not good. There is actually a graph of airspeeds and altitudes that shows an aircraft's safe operating envelope and the area you are describing (high altitude, max speed) is known as the "coffin corner". An aircraft relies on air to fly, as the air gets thin, you lose the lift you need to stay airborne, or you need to go even faster so you are getting more upward force from the limited air. All else being equal, you would eventually just reach a point where you cannot climb any further, all your "up" is being used to keep you where you are. The problem is, NOT "all else" is equal. The other thing that happens at high altitude is that your engine which is an air breathing engine (jet or piston, they both use atmospheric oxygen to burn their fuel) have less oxygen available, and can burn less fuel, and produce less power. Eventually, you no longer have enough air to climb and you no longer have enough air for your engine to maintain your speed and at this point your aircraft starts to become uncontrollable. You may enter aerodynamic stall, your engine may "flame out" and shutdown, or both!

Now I know what you're thinking, why not just use a rocket once you get to that point? Well, a few problems with that too. First of all, it takes a long time to get to that point. Secondly, rockets are heavy. If you need a big, heavy-lift plane to carry your space-plane for a long time, turns out that needs a lot of fuel anyway, and your rocket is going to have to be pretty small. But now it's going to have to haul not just itself, a 90+% fuel rocket, it also has to haul an airplane with dead-weight jet engines. So it can't be really small. It's going to have to be really big. Which means your heavy-lift airplane now has to be really, REALLY big. Ok, so detach from the airplane you say! Brilliant idea, this helps a bit, but not as much as you think. Yes, now you can have a small rocket again. But wait, rockets already do this! Rockets typically separate either a bunch of boosters, or a "second stage" at about the same point that an aircraft would be able to reach. So... you still end up about as inefficient as a rocket is going to be, you just took a lot longer to get there, it's a lot more complex, and you still have a really big bloody plane to deal with. For the record though, it's not impossible nor completely impractical. This is what Scaled Composites is doing. Maybe it will work, it hasn't been fully proven yet, but it's interesting, and potentially promising.

The short version of the answer can basically be boiled down to just be... for reaching orbit, you need a LOT of lateral speed. The atmosphere STRONGLY resists you trying to go any sort of supersonic speed, much less the incredibly hypersonic speed you need for orbit, and will either incinerate you, or force you to waste most of your fuel, or both. The fastest way out of the atmosphere is straight up. It may seem inefficient, and in some ways it is, but it is also necessary. The only mechanisms we have that are capable of reaching those altitudes to first escape the atmosphere so we don't incinerate ourselves and waste fuel, and then additionally reaching the extreme orbital speeds that are needed to orbit once the atmosphere is no longer a problem, without using heavy, complex, and vacuum-unsuitable air-brea

Ain't no air in space.