I don’t think he is a good logician
I think his trick is:
Basically highlighting a configuration of the ages where the answer to each of the statements is not-x because unlike the cases of the other permutations there is only one configuration of the ages satisfies this and so is the odd one out: BAC (the letters ABC are the initials of the name and the order of letters is the order of their age and NW are the answers to the questions in order if the configuration was true) :
But this
Actually tells them the configuration of their ages and so Bob would be embarrassed.