Details please 
I had booked one of the $365 "mistake" fares, and flights on my travel dates were cancelled due to the war. AA's travel alert allowed for making one change with no change fee or fare difference.
In the app, I was only presented with two new departure options: the day after my planned flight and the day after that, with no way to pick another date, despite the travel alert allowing changes through June 15. So I decided to chat via the app and see about picking other dates. Shortly after the agent connected and I explained what my problem was, there was a siren and we all rushed to the safe room. I was distracted and didn't notice that the return date I asked about was one day prior to what I actually needed (the flights from JFK leave shortly after midnight, so it doesn't actually count as a "day").
Literally minutes later, I chatted back in to fix the mistake, and was told to call instead. I called and the agent refused, as well as his supervisor (not to mention his terrible arrogance in chastising me "the policy allows for one free change, not one free change and another one a few minutes later"). I then tried Twitter, and that team also refused to help.
Then I tried a formal email to the main customer experience team. I received a "gracious" response allowing me to make another change --- but with fare difference. That was essentially no response at all and highly insulting as the agent clearly didn't bother reading my email or checking my ticket rules (I could have made a change with fare difference without any special permission). I replied back in nicer words to please review my email and ticket and all records again, as my grievance was left unaddressed. They replied that "it wouldn't be fair to others, sorry."
The following day, I called another phone rep. that refused to help. Then I just said "what the heck" and called one last time a few hours later, and started off the conversation with the agent in a very depressed manner ("I'm sure you can't help me at all since nobody else was willing to...").
Well, at first he said he couldn't help either. But then he said to wait a minute, checked something, and started asking me questions about how I made the change. So I told him it was via chat, and he said "Well you did it through chat because you probably didn't want to wait hours on the phone, right?"
Then it clicked: he was essentially trying to guide my train of thought and put the words in my mouth to get me to say that the mistake would not have occurred had I been able to do it myself on the site. So that's exactly what I said. He asked for my email, and after a brief hold, told me to take a look at what was sent: new tickets for the right dates!
After the dust settled, he said if I had done it myself, he couldn't have helped. But because there was manual intervention, he was able to explain that there was a misunderstanding and get approval. Food for thought if you ever need to make a change and want a YMMV semblance of Plan B to make one more change!
I was so upset because I literally contacted them minutes later, these flights have wide-open availability, and it was matter of one day and clearly a mistake. El Al (obviously not world renowned for their CS) was gracious enough to allow a change with no fee or fare difference on a recent flight, despite it being voluntary, and I didn't even have to ask for it!
I hope that didn't come across as entitled, and I do appreciate the fact that AA could have stood their ground, but my world view is that companies do not need to be run by robots as bureaucracies with no room for critical thought.
