I really don't know why you're having a go at me? I've stated multiple times what would have been a far more reasonable move here for the airline, and not once did it include dragging someone off.
I'm pretty certain airlines are legally covered as private entities to be able to in a cabin request someone leaves for just about
anything. You seem to be awfully naive about how detailed the small print is on an airline ticket. Legally, nearly every single thing in humanity will be covered, that's why lawyers and "small print" exist.
How airlines and other private companies choose to act is what brings PR heat and outrage. In this instance, whether they can ask someone to leave and demand it, after selecting randomly, has to be weighed up with just accepting this customer ain't budging, move on and select someone else and rinse/repeat until the plane can take off. It's not worth doubling down on an agitated person, even with them being randomly selected. Just move on and try someone else, and keep reminding the cabin the plane is not taking off till 4 people accept compensation.
https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec21
I mean, "an act of God" is even included
But yeah, I've cherry picked a few that will probably "stretch" to legally allow them to request you leave after you've audibly... refused to leave. Trust me, T&C are very meticulously governed and written in order to allow private companies to do just about
anything, especially in situations where you are getting compensation and either refunded or given another flight.