There's probably no issue in the world that everyone agrees on, some people still believe the earth's flat! When deciding what right for you and your dog, you have to look at lots of information, and try to find out where that information is coming from. In the past, men mostly, were dead set against neutering male dogs; I guess they take it too personally! People said they didn't want their dogs to change, but if you allow them to go fully through puberty, and mate, they will no doubt change; they are no longer a sweet little boy, but more like a raging hormones teenage boy. Some of the advice on not neutering comes from vets who are associated with breeding and showing, some of their advice might be given in the attempt to reduce breeders fears, I mean just because a dog isn't neutered it doesn't mean he will get cancer. Personally, I see the risk from automobile accidents the main threat. Joey would try to run out the front door every chance he got before he was neutered, after neutering training was so much easier.
My guess is your breeder wants you to breed because she would like to use your dog as a stud, someone else is taking care of her dog, yet she can use it however she sees fit. Does your breeder show; are their champs on both sides of the bloodline? If that's the case, you should have your dog evaluated by someone who does show and understands that only those dogs that fully meet standard, should be breed. We do have an overload of pets right now; millions of dogs are being put to death each day. Our yorkie rescues are turning away dogs, and people are continuing to breed, unhealthy dogs. You probably wonder what my motive is in encouraging you not to breed. Before I came to Yorkietalk, I was a lot like you, but in the past I bought a dog from a backyard breeder who didn't test for genetic illnesses and breed a pup that was too closely related to the father, when that's done the recessive gene has a chance to rear it's ugly head, and my little dog got a genetic illness that paralyzed him around the age of 6, he lived another year, but it was a really tough year for him and my children. The breeder wasn't a bad person, she just didn't know enough about breeding, you have to study this just like you do any hobby or profession, you can just hook up two dogs together, but that’s what most breeders do. There's an old saying, if you're not part of the solution, your part of the problem, so that's why I encourage others not to breed.
I just want to add that most of the advice you will see here is just from pet owners who love their dog, and want the best for them!