Why don’t people fly to Mars with a super fast plane?

Answer

No, that’s not possible. An airplane needs air to fly through. The wings of an aircraft are shaped in such a way that, at sufficient speed, they push the aircraft upwards, as a counter force against gravity.
An airplane cannot fly in a vacuum.

You can only give a spaceship from orbit around the earth such a speed in the right direction that it is “thrown” to Mars under the influence of the gravity of the sun and the planets. During the trip, the engines do not work! After all, that would require far too much fuel, making the rocket many, many times too heavy.

Suppose you want to throw a stone on the roof of a house: then you give it a sufficient speed in the right direction and that stone has no motor for the rest. Flying to Mars is actually the same: a spacecraft is given the necessary speed to reach Mars without any further engine. Only there is the engine briefly used to get into orbit around Mars.

But an airplane, no, that’s not possible. A rocket goes many times faster than an airplane.