This is an old wives tale, Studies have shown that shaving has no influence on density or thickness of the hair. After all the follicle is quite a bit deeper than the skin surface.
This fiction stems from the onset of shaving occurring basically at the same time as the need to shave. As we approach and then propel into the teen years the terminal hairs darken and coarsen. This results in a need to shave. There is then the perception that shaving causes the changes in the hair
Similarly, if a woman begins to develop darkening hair, more hair or coarse hair, the cause is hormonal; not because she began to shave.
Shaving also causes the hair to be struck at an angle, making the hair feel sharper and more coarse.