I do see this though:
Safety – Whenever refusal or removal of a Passenger may be necessary for the safety of such Passenger or other Passengers or members of the crew including, but not limited to:
Passengers whose conduct is disorderly, offensive, abusive, or violent;
Passengers who fail to comply with or interfere with the duties of the members of the flight crew, federal regulations, or security directives;
Passengers who assault any employee of UA, including the gate agents and flight crew, or any UA Passenger;
Passengers who, through and as a result of their conduct, cause a disturbance such that the captain or member of the cockpit crew must leave the cockpit in order to attend to the disturbance;
You do know that there were three other passengers that were "involuntarly" removed from the aircraft after boarding without incident, right?
The section you have posted are what some people have tried to use but it is not applicable because there was no saftey issue. He was neither disorderly, offensive, abusive, or violent.
The conditions of carriage are fairly long and I have posted them twice. I don’t think its fair to take up the bandwidth to post them again as they are on United’s site.
The short answer to your question is that when there are ~15 reasons you can be removed then if none of those reasons is true you can’t be removed. Otherwise they would have had a reason such as or any time the crew has a reason sufficient to them or they wouldn’t have bothered listing reasons just stated that the captain has sole authority and can remove you for any reason or no reason.
The section begins” UA shall have the right to refuse to transport or shall have the right to remove from the aircraft at any point, any Passenger for the following reasons:...
https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec21
The airline has right to ask you to volunteer but no right to force you. The people that left chose to do so, David Dao did not.