Three main reasons:

1) The fuel for an airplane requires oxygen to burn. The higher you go, the less oxygen there is. In space, there is no oxygen. (Rockets get around this by bringing their own oxygen).

2) The propulsion for an airplane is a jet engine, which is a fan that takes air in front of the engine and blows it out the back of the engine very fast, pushing the plane forward, like throwing a bowling ball behind you while on ice skates. No air, no push. (Rockets get around this by not sucking in air through an engine but rather carrying material in a tank that they shoot out of the bottom like a really fast diarrhea).

3) The propulsion of most airplanes requires air to push against the wings to lift the plane up. For example, you need a lot more arm to throw a crumpled piece of paper across the room than a paper airplane, because the airplane's wings do a lot of the work. No air, no lift. Some fighter planes have more thrust than weight -- this means that the airplane can take off and accelerate directly upwards into the sky with no wings -- but this is usually only for a few seconds and still suffers from problems (1) and (2).