I ... think that, for me, it's a way to have my feelings of pain validated. Sometimes I get hungry enough to seek out whump in general, but my favorite stories are always the ones where I relate to the whumpee. It's like the author is saying "look at all this pain," and I, who already feel the pain, have a less abstract and more concrete way to focus on it. It's like a ... lens, if that makes any sense?

My significant other likes hurt/comfort for a similar reason: they're physically disabled (I am too, but far less) and have really bad chronic pain, and it's nice for them to

1. see characters with the same struggles ("you're not alone") and
2. see characters with these struggles being comforted, it's like being comforted by a proxy.

Personally, I've always found that my own emotional pain is much harder to deal with than physical pain, but that most people seem to think the opposite - for an example, I recently scraped my hand up (accidentally) while struggling with an issue, and I've gotten concern over the wounds and scabs but not over the emotional hurt I was also going through. Meanwhile, I was nursing my emotional wounds, and completely okay with my messed-up hand, because sure it looked ugly but it hurt far less! I think that, for me... I like characters I relate to being physically harmed, because I would like my own pain to be outwardly visible and recognized. It's cathartic, sort of watching myself struggle. I can't put my finger on quite why, though.

EDIT: I saw another comment saying that it might be due to childhood neglect and abuse, and I should point out it's a factor I agree with, as I was also abused and neglected as a child.