If you need things boiled down to three word slogans before you can understand them this probably isn't going to help you.
A couple of years ago I would have said that the best evidence showed no statistically significant increase in adverse life outcomes for people who become sexually active at thirteen. So as long as they were having safe sex I wouldn't have said that there was an evidence-based reason to criminalise sex with them at that age as long as it was safe, consensual and so on.
(According to
this 6-8% of girls and 8-11% of boys in the USA claim to have had sex before they were fourteen. The age of consent is thirteen in Spain and with Romeo and Juliet Laws I believe there are quite a few other civilised jurisdictions where people can legally have sex at twelve or thirteen. So while thirteen is a shocking figure to some USians it's merely at the low end of the existing range of legal ages, and it's consistent with the low end of when children become sexually active whether you make it legal for them to do so or not. Sometimes we do want to criminalise "normal" human behaviour but it inevitably incurs a high social cost so you'd best have hard evidence that you are preventing more harm than you are causing).
However since some new and better-controlled studies have been done I think there's good reason to discourage people under fourteen from having sex, and less-good reason to discourage people under sixteen. So I'd now say that, since you have to draw a line somewhere, drawing a line around fifteen or sixteen seems like the least worst option.
On the other hand I don't think the available evidence supports going on a frothing witch hunt when you find people in the 13+ range having consensual sex. I think we should strongly discourage it but
we shouldn't get overexited and treat it like rape or murder.