As far as the actual act of driving is concerned, it is permissible per se for a woman to drive.
However, since driving for a woman breaches a number of Shar’ee laws governing Hijaab, etc. we say that it is not permissible for her to drive. We all know the opportunities of sin, shamelessness, unnecessary emergence from the home, etc. this brings about.
and Allah Ta’ala Knows Best
Mufti Muhammad Kadwa