They're using the Federal aviation system, public property airports, being routed by the FAA, and so on. It's much more analogous to requirements for auto safety and licensing.
The government can't mandate the color of your shirt in your own home, but they can mandate the exact shade of your turn signals when you're on public roads.
I'm not a fan of our current security state, it's insane. But air travel isn't a private act, it's important to calibrate the conversation to the issue actually at hand.