If this happens to me, then I would request that they formally notify security and have them come down to clear me. I have been accused and I think it'd be best for everyone, including myself, that the matter be explored.

How many would-be criminals or terrorists would call security down on themselves?

At the same time, though this is not a criminal proceeding, I would ask to be able to confront my accuser. It's a commonly recognized principle in American society.

I would also tell the airline agent that unless security finds something suspicious about me, they can expect a civil discrimination complaint to be filed against them for doing this.

And after security admits they have nothing to hold me on, or to accuse me of, I would then tell the airline that they better re-accomodate me or offer a full refund, plus compensation for the delay, and an apology on top of that.