> The barber in this town shaves all men who do not shave themselves. Does he shave himself?

I'm not familiar with this one but is it misstated here? The barber doesn't only shave men who don't shave themselves. If he doesn't shave himself then he shaves himself and therefore can shave himself without contradiction. If he shaves himself he can shave himself without contradiction. Either way he shaves himself.

(Or maybe I'm just bad at logic)

Yes you're right it's typically stated as "shaves all those, and those only, who do not..." https://en.wikipedia.org/wiki/Barber_paradox

I prefer the version that leaves the barber's gender unknown (i.e. could be a woman):

> The barb in this town shaves all men who do not shave themselves. Does the barber shave themself?