People should know how to brush things off and not be affected by other people's bs.
People can be able to do that and at the same time care about other people's feelings. In fact they can be better at it, and be able to show other people to deal with problems other people are giving them, and how to be a more confident person.
I don't think it's 'wrong' as such to feel sensitivity. It is an emotion, so how could it be wrong? I think it's a matter of dealing with that particular emotion; it's causes and side effects rather than simply feeling that way. If you cannot continue with your life due to your sensitivity, it may be an issue then, however, I still wouldn't deem it 'wrong'.
A lot of problems in this world today (socially) lie within our kindness to others. People often forget that others might be going through something extremely taxing without them knowing it. Often problems occur when people treat others cruelly (and sadly I see that very often in my school). Being sensitive can help with emotionally connecting to others (being sensitive to others feelings), treating others with kindness, and creating an all over comfortable and peaceful environment for people. Granted, there will still be conflict and mistreatment of others (due to human nature), but sensitivity can be a positive attribute to encourage. Although strength in what you believe in and other positive things must also be encouraged too. A nice balance of strength and sensitivity should be encouraged. :)