I would coach it as "self-loathing"!
Not sure it is a death wish so much as simply "not having a truck to give!"
Or maybe that is who she wants to be, because "the wold sucks" ... but, invariably, she ends up caring and trying to save someone or prevent something bad from happening!
It is this whole screwed up situation that makes her such an interesting character - the reluctant belligerent super hero!
She is the "Bizarro" Tick!