A friend just explained this to me, and in considerably more details (including how there're some songs with lyrics about how a middle school breakup still haunts one into ones twenties, things like that).

It sounded to me like many of them were suffering from some form of depression, but not getting therapy for it. In that case, emo's unhealthy because it gives them a subculture that enables their wallowing in depression, instead of seeking states of emotion that will enable them to do more about their issues and better accept the things they can't do anything about. Nothing wrong with such moods, only staying in them so that they disable you.

However, using it as a derogatory term apparently doesn't accomplish much. This same friend told me those emos she was talking about want you to wallow with them, or to kick them so they can have an excuse to wallow more.

At any rate, I've seen the word 'emo' applied to things far short of such severe degrees far too often.