The Barber's Paradox

Each man either shaves himself or is shaved by the barber. The barber only shaves men who don't shave themselves, who shaves the barber? Supposedly the barber can't shave himself because he only shaves men that don't shave themselves.

Well, why can't he shave himself? Only because you said he doesn't. That's not a paradox, that's just making up a set of rules that aren't logically consistent. I can make up logically inconsistent sets of rules too. All ducks have yellow feathers. This duck is all black. How is that possible when I said they all have yellow feathers? Cause it's a rule I just made up! Wow, what a paradox!

A true paradox is something like "this statement is false". If the statement is true, then it's false and if it's false, then it's true. There is no logical solution, it is a true inherent logical problem. The Barber's Paradox, on the other hand, is just making up logically contradicting rules and calling it a problem.