To each their own. I understand why one would think like this. I have cat-like tendencies, but I, myself, am not a cat and I am fully aware of that. I'm thinking that this is how an 'other-kin' thinks, only on a more....extreme level, (me + cat dreams + cat tendencies = I am a cat. This is how the thought process works out in my head, and how I'm understanding otherkins). The whole concept doesn't seem extreme, not saying that, but that's how I am understanding. You have tendencies to act/think like a different animal, therefore you must /be/ the animal. It's a bit odd, I'll admit, but nonetheless it's your belief, and that's okay. I don't know that it's something I believe in, but again, to each their own.
I, myself, am an accumulation of different beliefs based off of my own experiences and things I learn from different times/places/people. Not quite religious, as much as I am spiritual. If this helps you, spiritually, then I say: go right on believing that you're a dog. If it's not, then you'll be aware of that in time, and you should probably stop at some point. Either way, I come from a place of understanding.