Wouldn't it be safe to say that this trope could be called a subset of The Woobie? It's alternate title could be "Reluctant Woobie" or "Woobie in Denial," because this is when a character who incites sympathy in others resents the fact that people actually pity them. It also makes for some overlap with Jerkass Woobie, since biting people's heads off just because they feel sorry for you kind of comes off as being something of a bastard.