Is it normal i don't care much for anyones feelings?

I will first say I do care about people in general. I dont like seeing anyone get hurt and I wish everyone good things.
At the same time I don't have much empathy for anyones feelings. People say things such as their feelings are hurt or how can someone be so insensitive.
To me it seems like it is their weakness for getting upset rather than doing something about the problem. Nobody should be able to effect your feelings but yourself and if they cannot deal with it, it should not be mine or anyone elses problem.
This does effect my relationships with others but I just dont get why I should be burdened with someone elses feelings.