If you want to get really technical, Mormons are allowed to drink alcohol, though that does not change the fact that I have medical issues that would become worse if I drank alcohol. The idea that alcohol must be avoided is more of a recent idea, according to Alan Rock Waterman, a well-known person who was excommunicated, but still considers himself to be Mormon.
To get a good, though extremely long explanation of things, I suggest reading Alan’s blog post.
As for the brain damage, we are taught in schools here that alcohol kills brain cells, and that is where my remark of brain damage comes into play.