(This is not a guide for the cis. For that, please use Google, DuckDuckGo or whichever tickles your fancy)
"Closet" actually works, but it doesn't work the way gay people tend to think it does. I was closeted when I pretended to be a guy. I'm out now - no longer pretending to be something I'm not.
There's something else, too. I've actively dismantled the closet as much as I've been able to. I'd burn it down to complete oblivion if I could, but as it is, other people won't let me. They refuse to completely destroy the documentation identifying me as a male, or to completely rewrite it, for example (data integrity, identifying, blah-de-blah). Every time someone wants to interrogate me about my past (it doesn't happen very often, thankfully), that someone basically wants to re-erect a closet for me and, if not push me back there entirely, still remind me about the closet other people forced me to. The one I've done my damnedest to demolish.
What I think this all boils down to is that the majority doesn't want to admit to its mistake in sexing/gendering babies. The fact is, such errors happen, and there's plenty of us living proofs. The majority just needs to get over it, and start correcting its errors. Sans hand-wringing, please.