Why is it impossible for an astronaut inside an orbiting space station to go from one end to the other by walking normally?

In an orbiting space station, after one foot pushes off there isn't a friction force to move forward, so the astronaut will remain in place.

It is impossible to walk inside an orbiting space station because the gravitational force on the astronaut is zero.

In an orbiting space station, the astronaut and station are both free falling towards the earth, so pushing off the floor will send the astronaut "floating" within the station.

It is impossible to walk inside an orbiting space station because its rotation is too fast.