Unfortunately it’s not always that simple. In the tickets fine print you will often find that if they want to refuse service for whatever reason they can do it. Of course you can always settle in court, however most people don’t want or have the means to.
The law says you have to follow the orders of the captain, and that the captain has the right to remove you for safety purposes. An argument like this would be classed a potential safety issue.
When looking for the reasons behind the growing prevalence of security concerns in modern society (both from governments and companies), one can hardly avoid the conclusion that it's just the perfect justification for anything.
Sure it is, but that’s the law. Write your representatives to get it changed.
The way the passenger was removed was wrong, and potentially illegal (I assume you can’t shoot someone because they are trespassing on your property, presumably you can’t injure them either). I believe United paid some hush money to stop him suing, but I see nothing to show the captain wasn’t allowed to have him removed.
What happened may or may not have been legal (I would guess all involved parties, including the passive bystanders, did something illegal at some point); I believe the discussion is more about how badly the situation has been handled by the company, and consequently: can we trust those companies to operate an extra-judiciary blacklist of passengers?
This isn't hard.