That's not what genocide means. You can't come up with your own definition of a word then attack people for not using said made up definition.
That said genocide doesn't quite fit as it's not based on race or culture. Eugenics would be a more correct term.
Almost everyone cares deeply about their identity. People's identities just pull from different things.
An equivalent would be banning a certain sport or type of music or food type, etc. that people identify with.
If they tried to ban football or rock music you can bet a lot of people would lose their minds.