I'm going to call strangers fat in response to them calling me skinny
Do you think they might feel hurt by the names?
I'm sure they will be very insulted
I am sure they will be. I wish that society didn't feel the need to comment on the weight of people. You should not call them fat, just like they should not call you too skinny.
So I shouldn't call them fat since they would be hurt by that? I'm a pretty sensitive guy, so why don't I have the right to back at them?
No, it is wrong to hurt others even if they hurt you. You can be the bigger man and walk away. If it keeps bothering you you can see a therapist to help you work out your feelings and insecurities.