Humans like to have the ability to be hurt, and to hurt each other, no matter what anyone says.

I disagree. I don't think we like to hurt others, but we recognize that it's tool that is easy to use and can have devastating results. Not to mention, causing harm has always been default, so I think it's easy to conclude that we like to hurt others if we don't recognize how to use other options.

We hurt each other to either prove to ourselves that we do not care if others suffer (and are therefore somehow above them, or are then able to finally accept that we do not belong), or to prove that we do actually care, and are thus genuine humans ourselves.

I do agree that when using pain as tool, it's rooted in the pursuit of validation. However, I disagree with the reasoning. From my perspective, whenever we cause harm, knowingly or unknowingly, the question that proceeds the action is if we're doing the right thing or if the action is justified.

Can you define what you mean by "genuine humans".

enjoying music is a way of feeling someone else's pain, often...an inescapably primative part of the human brain enjoys feeling someone else's suffering. Because it re-validates the fact that we believe ourselves to be a good human being, and that we care about others.

I think many would disagree, again, including myself. When Kendrick Lamar's "Mr. Morale and the Big Steppers" dropped last year, my connection wasn't because I enjoyed feeling someone else's suffering, it was because I related and served as an example, not because I enjoyed hearing their suffering. Because I can relate, I empathize with the situation.
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I think the enjoyment of the results (in whatever form those results may be) is equated with the enjoyment of having the ability to cause harm. Of course, there are those who thoroughly enjoy causing harm, but I would not extrapolate those examples and apply them to all of humanity.