Elves are people too. They aren’t perfect. They can be bad parents, just like anyone else. If anything, their vaguely-chaotic tendencies might make such behavior more likely than humans, who have no such innate tendency.
Plus, abandoning a child is typically as much the result of circumstances as it is “bad parenting.” Biologically, human beings, and for this I think we can assume elves as well, have pretty strong protective instincts towards their young—those aren’t ignored lightly. And elven parents can find themselves in a bad situation where they feel forced to abandon the child, or are able to rationalize to themselves (or even be correct in thinking) that the child is better off with someone else, or what have you.
So anything that seems like a plausible situation in which human parents might abandon a child should probably be plausible for elven parents, too.