I think for tznius reasons, ONLY women should drive:
1. There is so much pritzus in the world that one has to look at if he is driving. Better for a woman to look at it while driving than a man.
2. Issur of bitul Torah- how can a man learn from his Gemara while trying to drive?
3. Much more tznius for a woman to drive her own car then to be out in public transportation.