Yes a BIG problem, if people are ending their pets lives simply because they are old and not wanted.
The only ethical use of euthanasia for pets is because they are suffering form an illness and are suffering with no reasonably hope of a cure.
Why is there a 'big difference' between chickens, beef vs puppies and kittiens and horses?
They are all animals just the same, and should all be treated with the proper care. Many cultures see dogs, kittens and horses as food animals also, not just pets. Same as now in America people are...