From a logical point of view what the barber does to men who do not shave themselves has no bearing on what he does to those who do shave themselves.

Sample syllogism:

  All crows are black. (All men who do not shave themselves are shaved by the barber)

  My black cat is not a crow. (The barber is not a man who does not shave himself)

  Therefore my black cat is not black. (Therefore the barber does not shave himself)

which we can see is invalid.