I think empathy is a very important ingredient to being funny and writing comedy.
In order to be very funny you have to have a sense of how people think and especially how an audience thinks, which I believe is not always the same thing.
However on stage you must appeal to both.
Having the talent to make an audience laugh but yet dig into them personally as individuals is extraordinary.
A good comedian seems to naturally know how to build tension and more importantly, when to release it for maximum effectiveness for laughs and minimum damage.
Great comics are born short winded storytellers.
Stand up is on purpose gossiping entwined with short emotional fits and rants.
A great joke has to have a compelling yet simple build (Set Up)
then a powerful twist payoff (Punch Line)
...most times revealing another story, a common truth, a lesson.