Because a right not to be offended requires a power to suppress offensiveness. The right to life and the right to property would be meaningless if murder and theft were decriminalized. In the same way, a right not to be offended implies that offensiveness must be punished.

The power to suppress murder is a relatively small power, and its limits are easily determined by laws and courts. A power to suppress offensiveness would be broad and vague, capable of suppressing anything anyone might object to. Since taking offense is so subjective, it would be difficult for this power to be administered by a neutral third party. It would be prone to abuses.

A right not to be offended requires an arbitrary power incompatible with freedom.

It seems straightforward from here:

Because empirically, history seems to tell us that very many people will always be "offended" by others disagreeing with them, or living/worshipping/looking differently.

And so if there were a right to not be offended, it would trample many of the fundamental human freedoms we associate with democracies.

Blacks and whites marrying offended some people. The River Brethren not going to war offended some people. And in this specific case? Black humor isn't that rate; Arsenic and Old Lace, man. I'm sure that offended some people.

The right to be offended probably can't exist in free democracies.

Because it necessarily limits the far more important right of free expression.

Not being able to offend/hurt feelings/be disrespectful would be contrary to any semblance of free speech.