All identity is a societal invention. That's the purpose of identity, it's for other people's perspectives and what they think. It's irrelevant otherwise, because what else needs to identify your gender? A dog? A stone? The clouds? And why gender of all things?

I'm a man. Apart from the basics, like a penis, I couldn't really tell you what "feeling like a man" actually is. Everything beyond the biological category is just made up stereotypes and don't serve any actual purpose. But for some people, they live by societal stereotypes, so if they don't like them, they will change their identity to fit into new ones. It's not at all necessary, but that's the power of worrying how others see you and why identities exist.

But at the end of the day, we're all just brains animating a corpse. So go wear a dress! They're comfy! More "men" should; they're missing out.