It's hard to say. I got most of my sex ed from my relatively liberal parents, or unfortunately even from the internet. That said, I think it should be the responsibility of the teachers, albeit with plenty of changes to the sex education curriculum.
For me, sex education was more like a basic biology lesson, only covering the mechanics of making a baby. There was no advice about consent, relationships or the emotional side of sex. And this was only a few years ago.
Contraception isn't just about preventing pregnancy. There needs to be more emphasis on preventing STI's, and it needs to be accessible to those who aren't heterosexual. I'm gay, so it wasn't like I was going to go round getting anyone pregnant.
As a gay guy, I often felt invisible during sex ed lessons. Everyone knew that I wasn't straight, but teachers continued to tell me all about how I could avoid getting a girl pregnant. Sure, heterosexual students vastly outnumber LGBT students, but we still constitute a small yet significant part of society - between 5-10% of the population, depending on which statistics you believe.
Would you be content with Maths lessons in which 5-10% of students aren't given calculators, or taught long division? What would you say about English lessons in which 5-10% students aren't given a book to read?
It's a silly analogy, but that's exactly what's going in sex ed lessons. LGBT students, and even many heterosexual students, aren't being given the tools they need to safely explore their sexuality.