This was more or less what I thought. Surely it should be the airport security who facilitate exit, not the airline? I did ask the BAA security people if I could leave by the way I came in but they told me I couldn't. I asked them on what authority they could hold me, to which they said if I argued then they would call the police. So I asked them to call the police, at which point they started to get quite aggressive.
We appear to be seeing the "rest" of the story.
You were never imprisoned. That doesn't happen in airports, save for those who commit criminal acts, or unusual circumstances when security dictates so.
You copped an attitude with the airline personnel, and it's little wonder that you didn't get what you wanted right away.
Nobody "broke a contract" with you. One cannot hold up a ticket and say "This ticket represents a contract, and I'm holding you to it...fly me there now."
Flights are always subject to change, or cancellation, and cancellation or delaying of a flight is right and proper when the conditions warrant. You can imagine, perhaps, the hazard that might be posed if as a pilot I were forced to make a flight, or take an airplane that might not be safe or ready to fly. From a pilot perspective, when I make a safety of flight decision, it's not open for debate or discussion, and it's subject to no "contract." There's no authority which exceeds the pilot's authority in making that call; it's final.
A passenger doesn't have that authority.
While I certainly agree that an airline--any airline--should do whatever it can, within it's power, to serve the customer...you don't own the airline, and you don't set the security rules and regulations. Not having been there it's hard to say, but your comments strongly suggest you became arguementative with the people in the terminal. When you ask "By what authority can you hold me," you're accusing those personnel of "holding" or imprisoning you...surely you understand how this might be offensive?
A passenger who is excited, difficult, argumentative, combative, or otherwise problematic is a safety risk. In the same way you don't really want to use certain key words in the terminal, you also don't want to cop an attitude, because it probably won't be tolerated well.
It's not exactly the same as your situation, but I'll give you the example anyway. Some years ago I had a flight from A to C with a technical fuel stop at B, in between. I had a single passenger; a friend of the owner of the company, an investor, and a part owner of the airplane I was flying. When we arrived for fuel, the fueler had mysteriously vanished, and the fuel was locked...no fuel. This meant calls to dispatch and a change in plans. The passenger, clearly inconvenienced, became irate. He began to scream and yell. He jumped up and down. He turned a reddish purple color, balled up his fists, and was spitting as he screamed at me. He told me to do exactly what he said, told me he owned me, told me to get in the airplane and fly him where he wanted to go.
I politely approached him and informed him that he was a safety risk, and that I had just grounded the airplane and cancelled the flight. This did not improve his attitude. I then contacted the company and informed them of the same.
A short time later he was able to regain his composure. I made alternate arrangements, diverted to a nearby airfield for fuel, and eventually took his destination.
I'm not suggesting that you're that person. That was a very extreme case; almost cartoon-esque in it's exaggerated behavior. However, it does illustrate the difference in perspective. From the passenger's perspective, he was paying a lot of money, and had a lot invested, and felt he had a lot of rights. From my perspective, it was a little different, as I explained to him:
"Sir, I appreciate your frustration, and can only apologize on behalf of the company for this situation. I am unable to take off and fly in search of fuel. We will need to make arrangements and a new flight plan to a location where we will fuel. Until that time, please let me offer you something to eat and drink and a quiet place to relax, and we shall be underway as soon as possible."
To my mind, that's customer service at the grass roots level. However, had we been in a location where secure procedures were in effect, I wouldn't have had that opportunity. He probably would have been arrested for his behavior, with or without my input. Being at the airport, in the terminal, in a secure location, becoming argumentative with the airport or airline personnel won't do anything to help your case; you can only dig yourself into a deeper hole. You may not like to hear this, but it's probably the best advice you can get all day. Yes, you're a paying customer, and yes, your patronage is valued and important. Yes, you're important. Yes, you deserve to be escorted promptly and if you wish, to receive a refund or a rebooking. HOWEVER...drop the attitude because it does not help you in any way...particularly not in the circumstances being discussed.
I've no doubt you're a good person who was placed in a frustrating situation. I've been there too...as I suspect have most others here. I can sympathize. I will conclude by saying that what you want at a time like that is to not make a frustrating situation worse...and cooperation goes much farther than conflict. Best of luck in the future.