Proverbs 12:10 states that " That the righteous one is caring for the life of his domestic animal, but the mercies of the wicked ones are cruel. The New World Translation renders the word life as the word soul. So maybe that is where this guy is coming from. I don't think that it will matter. The book is fairly clear that humans are to care for the animals in a kind caring manner, and likens anyone that doesn't as wicked or unrighteous. So that is what I would use as my biblical reasons for caring for unwanted animals. I have a few ideas as to why this repeated idea seems to leaking out of this guy, but that doesn't really need posted here. I am reasonably sure that the only way you will get this guy to shut up, and back off is quote from the book that he is so fond of. I would quote Prov 12:10 every time he starts, and not say anymore. Or I suppose that you can ask him why this idea is so important to him. It seems to mean a lot to him and bothers him. He also needs to take it up with his pastor, or one of Jehovah's Witnesses. I am sure any one of those people will be more than willing to discuss the idea at length with him. That last idea may shut him up or send him off on another rant.
Please note that I did read the OP's original post and all the rest of the posts. I have no interest in this. I will also not respond to any further discussion on this subject. This is a subjective opinion base off of a lifetime of knowledge. I would best describe myself as non-religious at this time, and I am happy with that.