No one has been able to prove that the frequency of haircuts affects their growth. This is an urban myth, nothing more. The only thing they say is that from frequent shaving, the hair can become darker and thicker at the base. And then, not to say that this is also a proven fact, and this is about shaving, not about a haircut.
Frequency of haircuts and hair growth rate are not related in any way. If the hairdresser told you so, then there are 2 options: - Either he is simply not competent in this matter.