My thought has always been that the first doctor was lying so long while pretending to be human that he just didn't completely weed the habit of referring to himself as human.
As far as the TV movie, my head canon is that he was expressing either a kinship via association, or referring to similarities between his species and humans. Either of which could be a good in-universe reasoning too.
It isn't like the doctor has to speak truth at all times. He's often shown misleading people, flashing psychic paper to outright fake identity, etc. He could absolutely make claims about being human or part human and it wouldn't be inconsistent for him to be lying for some reason.