My boyfriend's cat is sick-- I think he should put the cat down--- am I being cold-hearted?

IF he really does love the cat, he'll pay for he surgery, but if that's not an option he can either, have the cat put down,(its very common and it'd be best to put the cat out of it's misery) or spend a lot of time with the cat until it dies. You are not being cold-hearted, if anything, you are aware of what needs to be done so the cat can be happy. I hope I helped. Good Luck.