This argument would be valid if you could renounce US citizenship without first producing another citizenship. But it's not, and you can't. I never asked for a US citizenship, I don't want a US citizenship, and yet I'm bound by it and not free to revoke it.
This citizenship situation is more analogous to a slaveholder telling one of their slaves that they are technically free, because they are welcome to leave once they produce documented proof of ownership by another, different slaveholder. The slave is no sense actually free, despite the misleading, bad-faith assertions of the slaveholder and those who recognize the slaveholder's framework as inherently legitimate.
Imagine waking up at a car dealership that tells you that you MUST pay interest on a car whether you take possession of it or not, despite you never having signed any kind of contract with them, but they tell you that you are still free and nothing is wrong with the arrangement because they will let you off the hook for paying them as long as you can provide proof that you're bound to pay interest on another dealership's car instead. If you try to refuse paying the interest on the car you don't want and never agreed to buy, they will send a team of gunmen to your house in the middle of the night, throw a flashbang through your window, chain you up, and drag you to a cage they lock you in. They insist that the whole arrangement is perfectly fine because the people in the car dealership took a vote where they agreed to force you to be bound by those terms, and that's all the justification they feel they need.
Now imagine the same thing, but in addition to paying interest on the car you didn't want and never agreed to buy, you're also bound to help murder people at other car dealerships, too, at the discretion and whim of the car dealership you're currently being extorted by.
That doesn't sound completely insane to you?