"For one, nearly every animal can create a fertilized egg and at their core they're fairly indistinguishable."
"Fairly indistinguishable?" Nonsense. You prove that statement false with your next sentence:
"The difference is in a small part of DNA (of which humans share roughly 97 percent with other animals)."
DNA proves what species an organism belongs to - in other words, that small part of the DNA is the same 3% which will identify that organism as human for the rest of its life.
All the rest of your argument is nullified by this simple fact. An embryo created by two humans can only ever be a human embryo, as has been determined by modern genetics. If an organism naturally possesses human DNA, it is undeniably a human organism.