Every FT'ers mantra should be: if you don't like the answer you get, hang up and call back until you get an answer you like. And whatever you do, DON'T hunker down and stand your ground and bash heads with 'em. They'll notate your record and then you'll never get the problem solved. Just politely hang up, then call back and try a different AAgent.

You certainly have the right to change your plans in reaction to AA's schedule change. Key phrases to repeat politely include "that time just doesn't work for me" and "can you please help fix this?".