What about a computer that is sufficiently advanced to perfectly produce thought patterns and emotions that are of a type that are completely identical to those of humans? If you wouldn't recognize this as a person, I can think of only a few possibilities:
You aren't understanding, or are incapable of imagining, the concept of the machine that I'm talking about.
You have this weird tribalistic thing going on that is not very far removed from many of the justifications for racism. ("They just are different from us, and are therefore not deserving of the same status.")
You believe that humans have a soul, or something of that sort, and this supposed soul is what makes us people deserving of rights.
Is it one of these? Or is there another possibility I haven't considered?