I'm not theorising anyone's feelings away.
I think that people who are uncomfortable in their own skin should be given as much support as poss to make them feel happier, and that fundamentally society has to change to be more accepting of people with difference.
Assigning is not my term, it is one that seems to be used in the dialogue about these issues, and it seems useful.
WW do you believe that gender is a feeling, and a person's sex is determined by their gender?
You have said that boys who feel like girls are girls, and girls who just feel like people are people. This means that girls who are born female and just going about their business are not female, but a different category, of people? But others will identify them as female and treat them accordingly.
So how is this all to work then?