... if you aren't detained you are free to go. And if you are free to go, you are free to stay, unless the property owner has trespassed you. TSA doesn't own the airport, at least in my state. So how can they trespass you from the airport or otherwise continue to detain you from moving forward?

I mean, I know you're right, and I know you will always lose if you try, but I don't understand the legal basis.

I don't think it's a matter of whether or not you are free to go. It's a matter of whether they let you on the plane.

It's just federal law.

Cities don't own restaurants either but can fine them and close them if health inspections fail, because there's a law for that.

The legal basis is the federal laws written specifically around airport security.