[T]een daughter wants birth control but refuses to learn how to drive, is this weird?
No… not weird. Kids today are less likely to want a driver’s license right away. We don’t really know why. But this is documented all over the place, even including cities with crappy public transportation. My guess is that kids like being chauffeured and their parents are more willing to do it (and the current generation of dads are more involved with their kids) whereas boomer parents were less likely to drive kids places so they needed a car to get anywhere. But that’s completely uneducated based on no real research. Maybe it’s easier to walk places now and no reson to go to the mall. Who knows!
Even though teens are not more promiscuous compared to recent generations, apparently they’re being much better about using birth control. Long term birth control is also much better than it used to be. I also do not know why teen sex hasn’t changed (maybe a combination of a more permissive society being balanced out by more attentive parenting) or why kids are more likely to actually use birth control than in the past. My guess there would be a better job of culture making birth control seem normal (you can tell a hero is a good guy because he puts on a condom in romance novels and tv shows) although there is still an erosion of non-abstinence based education or planned parenthood in much of the country.
So… basically your teen daughter is completely normal for her generation!