The same right a business has to kick you out of their store. If you don't leave voluntarily, you will be forced out by those authorized to use force.
Just because a person has a ticket for a flight, that does not mean that person has a right to be on that flight. If United decides to remove a passenger for any legal reason, then United may do so and may request the police assist.
Absolutely, the airline was 100% in the right legally.
Ethically? PR wise? Yeah, not so much. The airline industry generally relies on public bailouts every couple decades to remain 'profitable'. Kicking customers TOO much in the teeth isn't the best business decision, even if generally you get the government to foot the bill if things don't work out. Generally, this isn't meant literally.
Airlines gamble on overbooking. They assume X percent of people will cancel, and they get to keep the cancellation fees. It's legal but DOT legally requires the airlines to ask for volunteers in exchange for compensation. Of course, the compensation isn't mandated, so it could be one stale peanut. Then yes, they can involuntary bump folks. That is actually regulated. If they get you to your destination within an hour, you don't get squat. If one to two hours, 200% of one way fare. >2 hours, 400%, but only up to a $1350 max. Offering $800 is significantly cheaper than offering $1350 because the government makes you do so. Airlines don't complain about 'burdensome regulations' because they know they make far more off gaming overbooking. That's even without folks forgetting to get written confirmations and filing appropriately for the compensation.
https://www.transportation.gov/airconsumer/fly-rightsJust because something is legal doesn't mean it's a smart idea. It's an optics issue. The airlines logically shouldn't expect happiness or sympathy from the public with the overbooking thing. Calling the cops on someone sane, mostly law bidding and rational is a wild card. In this case, the airlines lost because the Chicago cops acted like... well, Chicago cops. It's not 1990's LAPD, but still.
Mal: You called the Feds.
Jayne: I got pinched!
Mal: Which is what happens when you call the Feds.
Fairness and whatnot doesn't matter to the public. If the guy was an oil company exec or on his way to a furry convention, this wouldn't be a consideration. Doctor is respectable enough. Airlines aren't usually beloved. United should just be very very thankful they arranged to have an Asian minority beat down on their aircraft. I'm quite sure that as bad as this is, their CEO was very very grateful the Chicago cops didn't beat down a law abidding black man on camera in their aircraft. THAT would have been a truly epic PR situation.