I’m mostly with you, OP. First of all, the appropriate response from the agent after your second time correcting him should have been “sorry for misunderstanding you,” not questioning your motives for doing so. Not only is it none of his business, it honestly sounds as if he was being defensive, feeling indignant about having to be corrected so many times. Of course none of that should matter to you as a customer on the phone, who’s just trying to get his flights booked.

And as a non-native English speaker, I find it ridiculous and shameful that he decided to pull the accent card on you, of all things. I mean, is he not working as a customer service agent at an English call center? He doesn’t get to play that card when he’s the one that has struggled to understand what you’re saying, and thus failed to do his job properly.

That’s a ludicrously bad agent, and I pray that I never come across him. Obviously being courteous and nice to the agent is a good practice, but that doesn’t absolve the agent’s blame for his incompetence, and it’s understandable that you lost your temper.