Just out of curiosity OP, why are you shocked AA didn't hold the flight? AA's website says passengers are required to be at the gate 15 min prior to departure. Your inbound arrived inside that window, never mind when you actually made it to the gate. And if the flight was full, AA definitely had the perfect reason to remove you and give your seat to someone else. Frustrating for sure, and it wasn't your fault, but that's how it is.