Replace 'A' with 'The' and it works. Tbh I assumed people were already familiar with the Barber Paradox and didn't word it defensively, but if you take 'a barb

Replace 'A' with 'The' and it works. Tbh I assumed people were already familiar with the Barber Paradox and didn't word it defensively, but if you take 'a barber' as referring to a specific barber then it's a paradox.