people shouldn't be so sensitive to being told off.

I find this statement problematic -- what about those people who can't control their sensitivity? To them such a statement is like telling someone with untreated AD/HD that they just need to pay more attention, or that someone with untreated depression should just stop feeling sad.

Granted, this doesn't excuse such people from being jerks in response. My point is more that sensitivity and emotions/emotional regulation are more complex than you seem to give them credit for.