He probably wants to limit it to 5mm horizontal because more than that and you risk having a large labiomental groove.
Gunson likes to limit genios to around 5mm or so for this reason, too. There are always exceptions, like if your groove is totally flat to begin with, but yours isn't. Something else a good doctor should consider as well is how the muscles will stretch with that movement. It can feel very tight in that area with the wrong movements. His recommendation seems reasonable to me. I think it would be an improvement, though I have no idea what your expectations are.