Not really controversial in North America. In the eye of society at large and propagated by most dog pros only "serious" breeders, the ones that drag their pooches from one canine beauty contest to the next, should decide who does and doesn't mate.
Neutering is much less popular in Europe - and Western Europe does not have any more dog problems than North America, including behavior problems and pet overpopulation.

Hailed by humane societies as the solution to pet overpopulation, every surrendered and found stray mutt and purebred pooch is neutered. Including babies. I volunteered for a humane society that did not release a young male pup to his wonderful new parents, who had already signed him up for puppy classes, because his testicles didn't decent and he couldn't be neutered. So he sat in his run by himself during his most impressionable puppy weeks, instead of being in his home and learn things.
My suggestion to deal with overpopulation. Legislative changes that prohibits dogs being sold in pet stores, newspapers, parking lots and on e-bay. Large kennel breeders and puppy mills should be illegal. That is where overpopulation originates. People who breed for profit won't neuter.

Neutering as cancer prevention? Hm, let me see. The cancer rate in dogs is 43%, in some breeds higher. Most are neutered. Yes, a spayed female or castrated male can't get mammary or testicular cancer, but neutering does nothing to prevent all other forms, and might even increase the risk for some forms of cancer, for example bone cancer. Folks concerned about cancer should focus their attention to the gene pool, crappy food and our obsession with pest and insect free lawns and environments.
We are aware of the integral part sexual hormones have on human health. Think about menopause, menstrual cycles, puberty and andropause. How can we possibly believe that cutting such an important part of a dog's body out or off would contribute to homeostasis?

Neutering as a training tool? I work professionally with dogs since '95. Most of my clients' dogs are neutered. Most dogs that were surrendered to the humane societies I volunteered for had behavior problems. Most were neutered. Dogs have problems because they are bred and placed inappropriately, under socialized or socialized the wrong way, under or over stimulated, trained with alpha methods that teach aggression. With the exception of roaming and inter male aggression, castration does not solve behavior problems. And, female hormones are calming, which means a cranky female might even become more irritable if spayed.
The book "Stress in Dogs" (info on my book-list page at www.dogsensecommunications.com) indicates, based on a study, that intact dogs were less stressed than neutered ones. Which makes sense considering that the adrenal gland hormones interact with both the immune system and sexual hormones. Sexual glands and adrenal glands have a feedback loop to the control station - the pituitary gland. Eliminating sexual hormones has to affect the pituitary and adrenal glands and with it the balance of stress hormones and possibly the immune system - which plays a role in cancer.

Breed standards are made by humans, not dogs. Breeders decide who mates with whom based on their science. They have non-breeding contracts because the last thing they want is competition. That'll be the day I pay several thousand dollars for a dog and be told that I have to fix him/her. Some breeders completely disregard how the dog feels about mating; don't heed to signals a female gives that she refuses that particular male, or refuses to mate altogether. They disregard the knowledge the female has of her own body or what she sees in the male's subtle body language, or pheromones that tell her that he wouldn't be suitable to father a healthy and temperamentally sound litter. The breeder decides, and the female is either held and raped, or artificially inseminated.
The amount of congenital diseases and strung out dogs is proof that many "serious" breeders do not know better than nature.

Meanwhile we castrate and spay thousands of dogs deemed by humans not good enough to procreate. We are killing a whole species; a healthy and sound gene pool, in North America.
If we continue, what will be left in North America in 25 years? Only sickly, but beautiful looking dogs? Breeders already import purebreds to increase the gene pool. In a few decades we have to import healthy mutts as well.