Why is a young man called “son,” but a young woman is never called “daughter”?

To answer your last question first, yes, in my experience it is also exclusively used by men. There are approximate equivalents for girls/women (e.g. "lassie", "miss", "darl", "hun") though none so universal as "son" that I can think of. I wouldn't be able to give a reason why.

Yes to all of the above. Trying to answer "why" questions when it comes to language use can be such a juicy journey, but one that is invariably a closed loop....

I have heard an elder woman call a younger man son, but I think it was in a particular generational/cultural dialect usage. More often it does seem even to be the opposite: "Baby girl" can be interchangeably used with "little mama", "mamasita or mami", or even "boss lady". A boy-child enjoys the usage of "son" but a girl-child is not likewise called "daughter"; she is not "daughterized" but "motherized" instead....hmm....

I've heard young men who are similar in age use "son" with each other as an endearing term, or used to create emphasis, as they would the term "bro" or "brother".

Only on rare occasions have I heard "daughter" used by an elder woman when addressing a younger woman (who is not her blood daughter) and these were limited context - the elder was emphasizing the difference in age but acknowledging an intimacy of connection - speaking as a "mother" would and thereby implying a lesson in deference to the elder's words - justified by their disparity in chronological age - without creating social distance.

(I think the insult "son of a bitch" has more to do with insulting a man by denigrating his mother than with calling a man "son". And, a daughter of a bitch would also be a female dog, so literally would make more sense to say "bitch of a bitch". But I think all of those gender-related expletives really no longer have anything to do with gender and from of address; usages for "s.o.b." and "bastard" and "motherf-er" are all so generalized now.)