The travel agent sells tickets on behalf of the airline. The airline offers the fare, the agent sells it. Once the agent has sold the fare, the contract is between the airline and the passenger. You cannot enforce a contract of carriage against a travel agent. the travel agent doesn't have the planes. Nor, as you know, does the agent have the ability to bind the airline with some sort of special request the passenger may have.
The contract of carriage, and the ticket contract is not between the passenger and the travel agent. It is directly between the passenger and airline.
You are right - the basic concept is offer, acceptance and consideration. Then you prima facie have a contract. But as always, it's not usually that simple. There are a whole range of factors that can come into play which can void or alter a contract... duress, fraud, mistake, and overriding consumer law are some examples. And each of those has a whole range of differing circumstances that can come into play - when they might or might not apply, who the parties are etc etc.