OP was late for his CX flight and would not likely have been boarded as he didn't even arrive at ORD until T-25. OP cannot possibly know that CX would have held its flight for him. And, it's more than unlikely that it would have.

Beyond that, AA offered a rebook which apparently was inconvenient. But, OP accepted that rebook and didn't ask for anything else (and it's unclear that other Westbound routings were available).

The time to solve problems is on the spot. Now, OP is faced with a response from AA which will likely be that the incoming flight was late, OP misconnected and AA offered and OP accepted a reroute. Sounds harsh, but it's what happened and OP didn't do anything to make it better when he could have.