a person's gender (socially speaking) should simply be based on what they decide for themselves rather than some arbitrary characteristic of socialization.

Do you mean gender presentation or gender identity? If the latter, the "pick and choose" option seems quite harmful given that we're talking about a hierarchy. Men are the dominant, revered sex. Men are the default human. Girls are socialized into a woman-hating culture. Telling a girl who hates female gender stereotypes and gender presentation that her preferences mean she's really a boy or man is regressive, given that the female social and sexual role is considered inferior to the male one.

Instead of strong, aggressive, tough, masculine girls being told that their sex has nothing to do with their personality, they are instead being told that their personality may mean that they aren't really girls, that it's perfectly valid for them to choose to be a boy or man instead. Those of us who are left acknowledging our biological sex are then assumed to have a "cis" identity and are told that we feel aligned with those negative stereotypes.