Not satisfied completely with any of the answers, though C.S. Friedman and Michael Alvis are closer to my thinking, and Mack Moore and Kalo Miles are further.
Celia is closest in her initial formulation (which Michael does not contradict):
Opposites are paired items *in the same conceptual category*, with perfectly opposing (non-overlapping) qualities. To be one is to not be the other.
But the qualities not being overlapping is the most prototypical instance of opposition; you can have opposites on a cline, where there is no clear dividing line. The most clear instance of that is big and small, which are entirely subjective qualities (big and small relative to what?), and which are on a sorites scale (how many centimetres do you add to a dog’s height before it turns from small to big?)
So the fact that there is a cline of age, from infant to girl to maiden to woman to crone, is irrelevant. A woman can still be the opposite of a girl, particularly if we isolate the conceptual category as being not age, but (as Michael identified) womanhood, whether that is female + adulthood, or sexual maturity, or any of the murkier cultural constructs associated with girlhood and womanhood.
Mack’s notion that
The concept of “opposite” is geometric, geographic, or mathematical, not linguistic nor conceptual. In the observable world, few things have any actual opposite.
… well, I’ll just say that no linguist uses opposite in that extremely restrictive sense, and no layperson did either. If they did, big and small would not be opposites, because big and small are entirely conceptual and not geometric concepts (since they are subjective and contextual).
And “I’m an individual, I’m not a construct, you can’t put me in a pigeonhole”—that’s wishful thinking. Binary categories are how we understand the world. Intersex or queer individuals challenge the universal applicability of the binary category of gender; they don’t undo everyone else’s acceptance of that cultural construct for themselves.
I don’t like Michael’s answer, because I think the native speaker’s understanding of “opposite of girl” is far less refined most of the time. (It is, after all, a lay understanding.) But he is closer than Celia, in identifying that the conceptual category that the oppositeness is defined on is contextual, and in identifying several conceptual categories that it is aligned to.
If the context is sexual maturity, or adulthood, or other murkily related stuff, the opposite of girl is woman.
If the context is gender, the opposite of girl is boy.
By default? I’d say by default the opposite of girl is boy. There’s a reason Kalo Miles jumped to it. If for no other reason, because if you want to emphasise someone’s non-adulthood rather than their female gender, you don’t say “she’s only a girl!” You say “she’s only a child!”
EDIT: Oh, and the opposite wouldn’t be girls: we don’t consider inflection as making an opposite of a word. Opposites involve stems. Dictionary words, if you like. Baked in meaning.