False analogy. What happened is that United did not have legal basis to remove the passenger after he took his seat because they entered a contract with him by taking his money and agreeing to fly him to his destination. All airlines can remove passengers for certain reasons such as safety but none of those issues applies in this situation.
Whether they had the "legal" right to bump the passenger for its flight crew is still up for debate. Not at all settled. I for one do not want to leave that decision up to weary passengers at the time of flight who decide they don't want to follow the instructions of the airlines, who clearly believed they had the right to bump him.
So if a flight crew (wrongfully) tells someone that their suitcase is too big and must be checked (when technically it complies), that person should refuse to give up the bag or leave until the issue can be decided by a judge? I do not think there should have been a judge, jury, and appellate court all convened to finally settle the legal rights of the parties when Mr. Dao refused to leave. Whether contractually allowed or not, Republic Airline decided it had a need and right to remove the passenger from its aircraft, and he refused. If they were wrong he could sue of breach of the contract.
Moreover, the Chicago Aviation officers were not police and were not empowered to be on the plane and remove the passenger as they did.
I don't know where you are getting this. What does "empowered to be on the plane" mean? According to the City of Chicago, aviation officers can "temporarily detain and take people into custody until Chicago police arrive," and they are in fact off-duty police officers.
Bottom line is that airline passengers have certain legal rights because we are a nation of laws. Be glad that you cannot be thrown off planes and that you do not have to comply with unlawful orders by safety officers.
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And its not a false analogy at all. The airline and airport has policies and procedures in place, which is to defer to airport security when a passenger is not compliant with instructions. The airline contacted security and asked that the passenger be told to leave the plane. No one at the airline told the officers to bash his face in, and drag him off the plane on his back. There are no facts supporting a claim that the gate agents expected (or could conceivably have imagined) that security would rough the doctor up. Their experience is likely that passengers always get off when security arrives.