I think it depends on yr circumstances, how far away from shops/schools/friends etc you are, and how good public transport is where you live.
I learnt to drive 19 yrs ago, and it's one of the best things I have ever done. I'm glad I did it then, I don't think I could have afforded it now.
I hate relying on other people and really hate relying on other people regularly. Not to say all non drivers rely on other people, but for me, the idea of waiting in the freezing cold for a bus doesn't appeal. Neither does waiting another hr when the bus doesn't show which happens regularly where I am.
I am even less keen to use public transport after reading the thread on here about what goes on on buses/trains/tubes.
I live in a small village with crap public transport, and if people choose not to learn to drive, that's fine, but imo, it's only fine if they don't knock on my door week in week out to ask me for lifts/can I pop to the paypoint to pick up their electric/shopping/take them to the drs/dentists/mums/sisters etc etc.
I don't mind helping anyone in an emergency, but as a week in/week out thing, no.
The nearest hospital to me is about 15 miles away, and the nearest drs is about 8 miles away. We have no local shop, buses are not regular here after 6pm, and stop completely after 11pm and Sundays. This means that unless my neighbours have a car, they are stuck in the evenings and sundays unless they can afford a taxi or have someone who they can get a lift from.
Imo, my neighbours who have DC, especially young DC should learn to drive, purely because of our location, yet many of them dont.
As for sexes, it's important for both sexes to learn, can't see why it's more important for women.
I really really want my DS and DD to learn, but DS is not bothered atm. I'll keep trying to persuade him though.