Most of the tax breaks come from State and local governments. For example United Airlines gets a $20 million annual tax break on fuel purchases from the State of New Jersey alone. In 2012 the State of New York subsidized airlines to the tune of $227 million in tax breaks. These are separate from the AATF you mention.

Speaking of the AATF, sorry, but that goes against you too. International flights are charged at $18.30 (FY 2018) per person, per segment, and provide about $3.9 Billion of the $15 Billion in revenue collected. According to the DOT's Bureau of Transportation Statistics, in 2018 foreign carriers accounted for 52.4% of international passenger traffic to and from the U.S. and about 12.1% of total passengers in the U.S. air transportation system. Foreign airlines paid approximately $2.04 Billion of the $15 Billion raised by the AATF. So foreign carriers are contributing 13.6% of the funds for the AATF, but only carrying 12.1% of the passengers taxed by the fund, meaning foreign carriers are getting hit harder by the AATF than U.S. carriers are. Looks like U.S. airlines are getting subsidized by foreign carriers...

Regarding federal taxes, airlines have benefited greatly from the recent federal tax reform. In January 2018 Southwest airlines alone reported a $1.4 Billion benefit from federal tax reform. JetBlue reported $504 million in tax savings in Q4 2017. United's tax bill in Q4 2017 fell 95.9%.

That, my friend, is the "real world" which you talk about. Not this fantasy ALPA/A4A world you seem to be convinced is reality. So yes, I am sticking with that subsidy narrative. Still waiting to hear how you think chapter 11, which allows financially insolvent U.S. airlines to continue operating, shed their debts, and destroy their employment contracts, is not an unfair advantage to U.S. airlines.