Genuine concern and validation from others fills a basic human social need. I have heard arguments that pity is somehow demeaning but empathy is good, and yet the dictionary definitions are similar. Pity and sympathy are about feeling sorrow for another's misfortunes, empathy is about comprehending another person's thoughts and feelings (which could include pity/sympathy).

I think people who "don't want to be pitied" see pity as others being aware of their emotional state or misfortunes, while also seeing the pitied person as weak or unlucky somehow. That isn't the dictionary definition, but it's how some people apparently interpret "pity". We like to be understood, but not seen as a weak, unlucky, helpless person.

I can imagine that having others express obvious sorrow could cause some people to feel more self-conscious about what has happened to them and possibly feel judged somehow, which might cause a defensive interpretation on their part. It might be like "stop making me feel worse than I already am" for some people, even though their reaction to compassionate messages doesn't seem to make any sense from the outside.