Neutering won't affect his size, and it's absolutely the right thing to do for lots of reasons. Your Mom's right about it. An intact male dog is just about impossible to control when there's a female in season anywhere in the neighborhood; too many male dogs end up getting badly injured, either fighting over the female or being hit by cars when they're following her, or even being hurt or killed by irate neighbors. And you certainly don't want to contribute to the number of unplanned and irresponsible litters that result in so many dogs and puppies being abandoned and euthanized.