Is she a masochist? Her mental behaviour indicates that she is a masochist by obsessing with despair.
By performing the above she feels sexual despair pleasure I guess? Does it mean she's mentally extremely masochistic.
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I think she is neither of them, not Sadist nor Masochist (or maybe bother of them at the same time, depends on how we look at it). But she is crazy (I really mean mentally crazy) let me explain to you why.
What junko really loves isn't really hurting or being hurt, what she loves is the feeling of dispair, whether she is the one feeling it or making others feeling it. So if making someone or herself feel despair goes through hurting them or being hurt, then she won't hesitate to do so. But as I said , she is crazy, because she has a paradox that keeps looping in her mind. The paradox is that she want others to feel despair, but she also wants to feel despair as well, because her feeling despair makes her happy, but the problem is that in order to feel despair, she has to for exemple kill a loved one, but if we think about it if you love someone enough, then you don't kill him, but she would kill just for the sake of that despair. And the worse of all, is that even if you want to punish her for what she has done, you can't, because she would feel joy out of being in despair if you were to punish her. So she is a lost case, a crazy one at it.
So her mind is obcessed with despair not necessarily with masochism or sadism, she is just completely out of her mind.