From Harry's perspective, it would more be an explanation of why Wizards treat Muggles as a subhuman class than an argument to actually so treat them. After all, Harry cared about people (including, by default, Muggles) before he learnt about souls (or other forms of magic) at all, and what Wizards call ‘soul’ may end up having very little to do with what Muggles call ‘soul’. (All of this predicated on the assumption that Wizards actually mean something by that word, which Harry is so far not crediting, since Muggles don't.)

Also, it may yet be true that everybody (even Muggles) has a soul, although it would probably be simpler if only Wizards do.