United: "This man is trespassing on private property."
Chicago PD: "We'll be right over."
United breaking their agreement isn't illegal, but remaining on private property after you've been asked to leave by the people in charge is illegal.
That's like saying you leased your house to a tenant for a year but then six months in you find another tenant that you want so you call the cops on the first tenant. Doesn't work like that (well at least where I live).
A contract is a contract and nobody is tresassing here.
Sure, they're breaching contract, but that's a civil matter. It's completely unlike residency, as well, because that's got special protections, and as many times as people say this has special protections too, it doesn't.
To elaborate just a bit, breaking a contract isn't against the law, being "contractually obligated to let you stay on the plane" doesn't mean they can't kick you off the plane, at all.
The problem is lack of scrutiny by the officers handling this. The process should have gone something like this:
United: "Hey, we have this guy refusing the leave the airplane. Can you help us remove him?"
Chicago PD: "Why won't he leave the airplane?"
United: "He says he needs to catch this flight for something work-related."
Chicago PD: "Is he threatening other passengers? Why do you need to remove him?"
United: "We need to fill the seat for some last-minute flight crew. Look, this is really important, can't you just come and take this guy for us? It's already becoming something of a scene."
Chicago PD: "So what you are saying is, you are asking a paying passenger who is already seated in a departing plane to leave. And he won't do so voluntarily. Can't you ask someone else to go instead?"
United: "We tried, but no one is willing to take less than $1600 worth of our $50 flight coupons. Ridiculous! We do no more than $1200 per FAA guidelines."
Chicago PD: "But did he break any laws?"
United: "Not sure, maybe there's something in the ToS."
Chicago PD: Click