So there are a few issues to clarify here, but first, a disclaimer: I am not an expert on the law, and will not be speaking from the point of view of interpreting the law.
That said, however, it does seem to me that an "age of consent" is an appropriate legal construct. The idea is that 13-14 year old children have simply not developed far enough, not just morally, but most importantly neurologically, to be very good yet at forecasting consequences of their actions. With respect to issues like sex, it is not unreasonable to think that if young teenagers are not yet capable of forecasting consequences of their actions--by which I mean not just being able to think or say, "I might get pregnant," or "I could catch some STD," but actually appreciate what such an outcome would mean for them--then they are reasonably thought not to have what it takes to give genuine (i.e. morally significant) consent. Of course, many girls that age know about sex, and some even have sexual fantasies. Some, given the opportunity to do so, would also agree to have sex with someone they were interested in. But such understanding, desire, and agreement cannot count as consent in the morally significant way, so long as they are incapable of really appreciating what they are (or might be) getting themselves into in terms of consequences.
This same reasoning applies to age-limits for signing legal contracts, drinking alcohol, smoking products, driving, enlisting in the military, and voting, just to name a few. The age limits are different for some of these, but the basic reasoning is similar in all cases: we think that such activities require certain levels of responsibility about consequences, and we think that below certain ages, it is not reasonable to think that young people can be responsible in the appropriate way.
By the way, I think what you say about boys is simply mistaken. An adult woman (no less than a man) who has sex with a 13- or 14-year old boy would commit statutory rape under the law. The issue is not whether or not 13- or 14-year old children are capable of having sex (physically). I assume most are. But that's not the issue and besides the point, which, again, has to do with being able to manage responsibility.