Identification has two components: recognition and authentication.

I'm not an expert on neural networks, but from what all I've heard, current systems can only be trained to be really good at doing the former.

I once used to have a tabby cat. When it ran away, I put up posters with a picture and description. I got several calls about cats in the neighbourhood that had the same tabby colour scheme (recognition). And from a distance they indeed looked the same. But close up, they each had a different eye colour, colour of the nose, or length of its white "socks" on its paws. (authentication)

To do the second step, the system would need to be trained not just on raw pixel data but also on which features to look for to distinguish one cat from another. I think that current system could be brute-forced to do this, somewhat, by training also on negative examples ... but I feel like that is suboptimal.