Your comment itself is contradictory is it not? If I am to understand "Also, wtf?" to mean something like "euthanising dogs is immoral because it shortens their life", your other argument is that sterilisation is superior because it essentially starves the other dogs. How is starvation morally superior to euthanasia?
Caveat: I actually also have the same emotional knee-jerk response. I own and love a dog very dearly, and the idea of just "getting rid of all the dogs" doesn't sit well with me.