I'm going to disagree with everyone here.

Clearly, more time would have been a good idea. And UA has no responsibility to get you thru security quickly. But that said...

I'd take a good long look at UA's contract of carriage and other policies from their website. If their policy says checked-in passengers need to be at the gate/on board 10 minutes before departure, and you were there 11 before, then you have a valid complaint. There was a similar complaint on the AA forum a few weeks ago, and posters there were lining up to support the poster.

I'd send a written complaint to UA with the appropriate part of the contract of carriage to UA, and request the standard compensation for "Involuntarily Denied Boarding". Don't focus on the rudeness. You can mention your status, but don't focus on it, elites have the same timetable as everyone else. Stick to the fact that you met their requirements, but were not able to bet on your flight.

Of course, you may have difficulty proving what time you arroved at the gate, for example, they may suggest that your watch was a couple of minutes off. Not sure what to do then.

But that's the letter I'd write. Good luck, and next time, leave a bit earlier.