That's not the same logic though. His logic is "Noun A is part of noun AB, that does not mean noun AB is equal to or a subset of A." While the way you're interpreting it is "Noun A is part of noun AB, thus AB is not equal to and not a subset of A." The important part is that his logic only dictates that the relationship between A and AB are independent of eachother, while your interpretation states that A depends on AB in an inverse manner. Ie: "We cannot say popcorn is or is not corn based on name alone," vs "popcorn cannot be corn because corn is in the name."
Not taking a side on social justice, the logical comparison you attempted just bothered me. Thank you for coming to my Ted Talk.
Just in case this isn't a bit: OP, the structure in English should be "adjective noun." The opposite to most romantic languages where you say the noun then the description word. So a cat girl is a girl (assumed human) that can be described as a cat (has the traits of a cat). A girl cat is more reasonably a cat that is a girl, though you'd probably say "female cat" more often. For allergies you'd want to look into hypoallergenic cats like the hairless sphynx.