I'd be against putting my daughter on birth control for a few reasons. I've heard a few horror stories from girls that went on birth control at a young age and when they came off and wanted to get pregnant, they had problems. While their bodies are still changing there could be a risk for perminet damage.
The other reason is that teenagers think they're invincible a lot of the time. He or she (or both) might think that just because she's on birth control, nothing bad will happen. What if he picks up an STD and passes it to her? What if her body chemistry changes or she forgets to take the pill and she gets pregnant? I know there's alternatives to the pill, but the birth control still might fail her. My gf was on the pill and I have a 4 1/2 year old son.