You appear to be conflating several identifiably distinct things (e.g. identity, sexual orientation, role in society) under the label of "gender" and then wonde

You appear to be conflating several identifiably distinct things (e.g. identity, sexual orientation, role in society) under the label of "gender" and then wondering why people seem to treat them differently even though you've applied the same label to all of them. The contradiction is an artifact of your measurement technique. It's still a developing field of study, but AFAIK the current thinking based on the evidence is that gender roles are largely social constructs while gender identity is at least partly based in biology (that is, the brain has some innate conception of gender even if many of the implications of those genders are filled in by society). And sexual orientation is yet another separate thing.