Qatar Airways would love to work more closely with a US partner to feed its flights. They’d love to solve political problems in the US where Delta, American, and United are trying to get the government to shut down their flights. Tensions in the Gulf region mean they cannot even work with the UAE on that effort. Indeed, they’d love the help of the United States to reduce those tensions.
A bid to purchase a stake in American Airlines seemed like a way to move the ball on all of those objectives, much like their major ownership position in British Airways and Iberia parent IAG has benefited them.