Actually, he did, the moment he refused to exit the plane with the Captain order, he is interfering the flight operation, and by that time he has both broken the UA Contract of Carriage (Rule 21) and the US Code 49, interfering with Flight Crew and Attendant.
What you are thinking is that, the order from the Captain is not reasonable to comply, why I have to disembark from the plane when the other get to travel, however, being reasonable is not of a concern, The pilot's instruction is legitimate, because he is not telling Mr Dao to take off his cloth and get naked or get into the storage compartment. He is asking the pax to get off his plane, the reason behind this instruction may be within or without reason. (In fact, the Captain can ask you to leave anytime he wanted with or without as valid reason) That order from the Captain is legitimate, and being unreasonable is another issue.
In reality, if all law have been follow, and Mr Dao Leave the plane, and then compliant to the UA or FAA about this, he would have a case, maybe he can sue both FAA and UA for a hefty compensation to remove him without reason, but in the end, this is not the path he choose, he choose to stay in the plane even tho the instruction from the pilot is for him to leave, and that instruction is valid and legal. He broken the law then, and he is in the wrong in this situation.
In deed, race have played an important part.
My wife just told me in the year of 2015, 6 out of 100,000 pax was forcibly remove from flight in the US for all sort of reason, judging that there are 40 millions traveller by air, that mean there are at least 2,000 pax have been removed in 2015, yet nobody ever heard about it, but this?
What make this different is race. As I said, even my wife kick pax out of plane before, it is not an uncommon issue, just that dude pus the time plus a bunch of people think it's inappropriate (Which is not actually) that put the story together.
This should not be a "Trial by Media" case, in fact, I would like to see Dr Dao being charged with Interference with Flight Operation.