I'm horrified by a lot of these responses and also by what you wrote OP. A lot of posters are using it to have a go at the mum and completely bypassing how this situation came about.
I don't think that if a SC comes to you for contraception advice it's overstepping exactly.
However, THIS, is hugely overstepping:
I happened to say (I didn't meant this at her in particular) that I think all girls should go on contraception as it prevents any little mishaps that are bound to happen.
You just "happened" to say it to a 15.5 year old teenage girl who is impressionable. You should be more careful about what you say. I vehemently disagree with this view because like other PP I've had serious detrimental consequences from the implant and the pill didn't agree with me either. There have been class action law suits about the implant and other types of hormonal contraception. Your SD isn't sexually active, there's no pay off at the moment for taking the risk. I also think it's a misogynistic view. I would be furious with you if I was her mother.
For the record she's 100% not sexually active yet but it only takes that one night with the boy she falls for.. one of her friends has openly had 2 terminations so she's very aware of that option also but doesn't agree with it.
It does only take that one night with the boy she falls for. But how about talking to her about the risks, making sure she's ready, making sure HE is prepared, talking about how it doesn't stop the risk of STDs?
I am vehemently against girls or women going on hormonal contraception unless there is a medical reason, e.g. periods. Your view is different to that, but your view is encouraging your SD to put herself at potential risk of side effects and potentially to minimise the need for focusing on all the different ways sex can not be a good idea, besides the risk of pregnancy.