I wanted to go on birth control when I was a teenager. It had very little to do with sex, really. I did want to have sex with my then-boyfriend, but whether I had access to birth control pills or not wasn't really going to impact that decision. I had condoms and, to my under developed teenage brain, that was all we really needed. We never actually had sex, by the way, but that's not really relevant.
I wanted birth control because I had awful cramps. Not cramps that kept me home from school, mind you, but that's mostly because my parents didn't think that was a good enough reason to miss school, so I had to stick a Thermacare heating pad in my underwear and suck it up. But dear god they were awful. Not to mention my other symptoms, and of course my acne, which I didn't have a problem with most of the time in high school, but still, birth control could have helped with that. But my mom was too worried about me having sex to let me get on the pill until I was 18 and about to head off to college.
Honestly, whether someone can get birth control probably won't make or break their decision to have sex. It might for some people, but for most people (I think), if birth control pills are inaccessible they're just going to use condoms. And the only barrier to condoms, other than the fact that they cost money, is that some pharmacies in low income areas keep them under lock and key and you need a sales associate to get them for you, kind of like whitening strips and razor blades. Even if buying them is embarrassing, I have not heard one story of a sales associate saying "sorry, I'm Catholic" and refusing service. I'm sure it's happened somewhere at some point, but clearly it's not all over the internet. The only thing restricting access to birth control does is make sex less safe and unplanned pregnancy more prevalent. I'm not saying that restricting access to birth control isn't a problem, it certainly is, all I'm saying is that restricting it because you think it'll keep people from having sex is flawed logic. So you're limiting reproductive freedom based on flawed logic, not to mention an archaic reason. It's not the government's business, or my employer's business (Catholic or not) whether I have sex.
Okay at this point I'm just covering my bases so no one reads this and says "but you forgot THIS reason why barriers to birth control are bad" or "no no no, that's not THE reason why it's bad," I get that there are several reasons why the government should stay out of my lady business, I just really don't feel like listing all of them here when I really wanted to connect my personal experiences with the larger issue at hand.