Because it pushes aside all his work. He is working on a perfect bite, usually for cosmetic reasons, but also because the lifetime of the teeth supposedly is enhanced with correct and straight teeth. The clarinet really doesn't work well with all those hooks and wires in there. If the dentist is careful and has been educated in aspects concerning the clarinet, he may try to cover all of that hardware with more wax and smoothness so that the aspiring clarinetist will not encounter too much discomfort coping with the dynamics of the positioning of the lips around or against the teeth in embouchure development. If the dentist has not, or even if the dentist has, they still may even make it more uncomfortable.
Braces cost parents thousands.
So indeed, do clarinet lessons. It usually depends on how much you MUST play the clarinet. And then, when you have all those nice straight Hollywood teeth and your richer dentist pulls off his prosthesis, you will probably have to make further adjustments. The thing to remember is that, while these adjustments, the braces, the health of your mouth and teeth are terribly important to all those concerned, they are very small amounts of time and discomfort within the musical life about to be undertaken. Which means, it CAN be done with braces.