The real secret origin of the Teen Titans
In their first adventure Robin, Aqualad, and Kid Flash are thrown together by circumstance and become friends. They decide to form their own little club and the only other person they invite to join is a girl that none of them is interested in or has ever apparently met before. How did that come about then? (2)
So maybe they all secretly have the hots for her but they are intimidated by her much higher power levels, and daren't make a move on her for fear of getting their arms broken and dropped from a great height, but I think the answer might be much simpler and more logical.
The Justice League of America's original lineup (3) was Superman, Batman, Wonder Woman, Martian Manhunter, Aquaman, and Flash. Of these six, four had teenage dependants (4), who are Aqualad, Robin, Kid Flash, and Wonder Girl (5). They never get to go along on JLA adventures, so where are they when JLA stuff is going on?
You know what it's like when you are a kid and your parents get together with some other kids' parents and you are forced to spend all afternoon with a bunch of kids you don't know, don't like, and would never be in the same room with if you had the choice? That's what the Titans are, and that's why Wonder Girl is a member. The Teen Titans is the Justice League's day care center.
1) Actually there's plenty that makes no sense to me, but this question keeps recurring.
2) I am aware there is a later retcon in which all four teen heroes are thrown together by circumstance, but I'm not buying it.
3) ignoring retcons.
4) technically five, but Superman has stuck his young cousin away in an orphanage and is pretending she doesn't exist so he can keep milking the "last survivor of Krypton" thing.
5) Wonder Woman's relationship with Wonder Girl is a lot more complicated since they are both the same person, and in fact Wonder Girl had been retconned out of Wonder Woman completely before Teen Titans #1 was even published, but that's a whole other story. Come to think of it, it must be at least 10 years before Wonder Girl is ever mentioned again in Wonder Woman, by which time they've forgotten she doesn't exist.