The clue's in the name: airplanes need air for lift and to run their engines. There is no air in space.

Rockets don't need air, they get their lift from their rocket engines which carry their own fuel-oxygen mixture.

Two main reasons:

(i) to get to space you need to escape earths gravity completely which requires much more energy than just flying above the surface as regular planes do. You need a shed load more fuel and so need big fuel tanks; and

(ii) travelling through Earths atmosphere is crazy destructive (that’s why things burn up coming back down to earth) so you need special design to withstand the heat.

TLDR: planes don’t go very high compared to rockets.

Airplane wings need to have air around them in order to generate lift. The air which passes over the wing moves faster and at a lower pressure than the air which passes below the wing.

Airplane engines are designed to pull or push the airplane through air. If the air is too thin, or if there is no air, then the engine has nothing to push against.

The key reason you're missing is that planes generate lift by moving through the air. As they fly higher, the air is thinner, and thus produces less lift. Planes would eventually reach an altitude where they can no longer climb because they can no longer generate enough lift to climb any higher.

Ahh yes. I was thrown by OPs comment about the fuel tanks…

… Three main reasons haha

An airplane engine is basically a giant fan that pushes a huge amount of air backwards, which pushes the plane forward and upward.

As you go higher, the air gets thinner and thinner. As you go toward space, airplane engines lose power as they have less and less air to push. (And if you have a jet engine like most modern passenger aircraft, it needs a certain minimum amount of airflow to run at all.)

Airplane engines require air to work, that is conspicuously lacking in space. A rocket plane could go to space.

Engines propel by moving molecules from the front of the craft to the back of the craft, hence using a turbofan (move air from front to back with a fan powered by a turbine) or a rocket (blow a mixture of hydrogen and oxygen from the front of the craft out the rear) - a rocket can work in space because I am not relying on atmospheric mass (the air molecules) for propulsion. In space, gas molecules are too far apart for this to work.

The term for this is 'reaction mass' or 'where do I get stuff to toss behind me to make me go forward?'

Airplanes need an atmosphere (aka, ‘air’) to rise up into the sky (aka, ‘fly’), just like a boat needs water to float and move around.

So an airplane could fly on Mars (let’s say it’s battery powered so we can ignore fuel) because Mars has an atmosphere.

But on the Moon an airplane would never be able to lift off of the ground, no matter how fast it was moving, because there is no atmosphere for it to push off of and ‘float’ through (on top of that, but keep in mind it’s a separate issue, turbines and propellers would also be useless on the moon).

Here is a weird fact: Air and water are both considered ‘fluids’, therefore the same principle that lets airplanes fly also works underwater!

Conclusion: Airplanes cannot leave Earth’s atmosphere because they require it to operate, and in more ways than one!

Yeah I suspected it was something along these lines. Thank you for explaining it in better detail.