I don't use many of the complicated hairdressing services, so I thought that it was mostly about ensuring that they all knew about the health rules. For instance you don't want any tools used on your head to have bacteria or parasite eggs on them. Nor do you want to be cut by a dirty scissor.
When I saw another commenter's report on the two years of college required to get a cosmetology license in a certain US state, though, that level of education seemed to be quite a high requirement for someone who simply wanted to open a barber's shop.