I'm a Christian. The analogy is not "inflammatory" to me, does not "incense" me, and does not "piss me off."
Two things come to mind, though. One thing is that for a better analogy, it should not read that the breeder sent his son (period) but that he sent his son in the form of that same breed of dog. And this goes along with what one other user commented about the issue of communication.
The other thing is that Jesus claimed he and the Father were one. In the analogy, the son-dog that the breeder sends would have to be one with the breeder. So the breeder is incurring the wrath/pain/agony/punishment/etc just as much as the son-dog is.
PS - Greetings, this is my first post.