my question is how is AA disadvantaged by the ME3 if they refuse to put any metal to the region?

Large market share loss to the Indian subcontinent, loss of European partners market share and Tim Clark's publicly stated goal to pepper the skies with A380 service to many large American cities. If the ME3 carriers are allowed to continue at present expansion rates the US Majors will become mostly domestic and niche International carriers as they offer a far inferior product and service level. EK is here for the long haul but long term depressed oil prices may slow EY and Qatar.

Exclusive: U.S. airlines disclose details of bookings lost to Gulf carriers | Reuters