It's called the
Argumentum ad Misericordiam (
argument from pity or misery), which is the fallacy committed when pity or a related emotion such as sympathy or compassion is appealed to for the sake of getting a conclusion accepted. The usual conclusion I have encountered goes something like
"They have it bad, thus you don't have it bad at all".
I once complained to a church leader that I was unpopular, had no friends, couldn't get a girlfriend, et cetera, ad nauseum (just like about a dozen other members on this website do now). She took me to a nursing home and introduced me to person after person who had seriously physical, emotional, and mental problems. At the end of the "tour", she turned to me and asked,
"There; now don't you feel ashamed of yourself?"Gee, thanks a lot, you sanctimonious, holier-than-thou, two-legged female canine (or words to that effect).
I never talked to her again; nor did I ever return to that church. I didn't go to
any church for a few decades after that, either.
... anyway ... what were we talking about again ... ?

Thanks, I was actually looking for the latin name of the logical fallacy, but could not find it using google.
I hate logical fallacies. Some logical fallacies should result in fines!