Putting aside the pain it would cause dog owners to have their pets put down --- which I agree is a meaningful concern --- would we still be obligated ethically to end the suffering of these dogs?

For instance, to refine the point: some decent number of brachy purebred dogs are currently in shelters (usually, specialized shelters). Those dogs have no owners and the human emotional pain that would be inflicted by euthanizing them is minimal. Should those dogs be put down, rather than rehomed? Bear in mind that it's actually pretty difficult to acquire a homeless purebred brachycephalic dog; they're in demand.

(We tried; our older dog is a rescue and we'd hoped to rescue an older purebred as well).

I'd say the desire for the dog to live should be considered. That is, even if (b) has zero weight, (a) can outweigh (c)

Can you help me understand how an extant dog could have a desire to live so ethically powerful that it overrides suffering, while it being simultaneously the case that it is unethical to bring such a dog into existence? It seems to me that your (a) implies that a living dog suffering from these defects is generating some benefit from living. Isn't it: maximum benefit > some benefit > no benefit?

That's a good question. I suppose I'm arguing for ethical framework in which I'm not the sole judge of costs and benefits.

I think the pug will suffer so much that its life is not worth living. But if the pug feels differently then to some degree I should respect that.

I guess my view is shaped by my empathy for the dog. How would I feel in his situation? Similarly, if I end up in a hospital bed racked with pain, do I want the doctor to make a cost-benefit analysis without regard for my own feelings?

Respectfully I want to creep up towards a presumptuous argument and say that you won't argue for euthanizing pugs because your gut tells you that whatever trouble pugs have due to their (many) health problems, a well-cared-for pug is generally a happy dog, and is not in fact living a life of overwhelming suffering.

We own a rescue mutt and a brachy purebred, and while I can't get inside the heads of either of my dogs, I would have absolutely no trouble telling you which of the two dogs is enjoying its life more. :)