There is a barber in a village. He said that he cut all the people in the village who didn't cut their hair. So should he cut his hair?

If he cuts his own hair, then he is not a "person who doesn't cut his own hair", so he can't cut this person (that is, him).

If he doesn't cut his own hair, then he is a "person who doesn't cut his own hair". According to his conditions, he should cut his own hair.

This is a paradox, no matter how you choose, it is wrong.