Let’s start by stating the barber paradox, based on Russel’s paradox:

“The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself?

Answering this question results in a contradiction. The barber cannot shave himself as he only shaves those who do not shave themselves. As such, if he shaves himself he ceases to be the barber. Conversely, if the barber does not shave himself, then he fits into the group of people who would be shaved by the barber, and thus, as the barber, he must shave himself.”

Source

Here is a puzzle for you – does the following ‘work’? I mean can you switch out the concept of shaving, and use ‘laughing’ instead…

“The comedian is the “one who laughs at all those, and those only, who do not laugh at themselves.”

The question is “does the comedian laugh at himself?”

Let’s take the analysis text above and shift the example from a barber to the comedian:

The comedian cannot laugh at himself as he only laughs at those who do not laugh at themselves. As such, if he laughs at himself he ceases to be the comedian. Conversely, if the comedian does not laugh at himself, then he fits into the group of people who would be laughed at by the comedian, and thus, as the comedian, he must laugh at himself.” Hence we have the contradiction.

So – if in any way – why is this different to the ‘barber’ example?
Offering one suggestion, it would be that ‘laughing at yourself’ is an internal, ‘turning backwards’ upon yourself’ process; internal, not external.

And sure, you can switch out ‘comedian’ to e.g. person, which may make a difference too. No jokes here, just playing with ideas.