If Routh was/is a muslime, the reason for killing Kyle is pretty easy to figure out. They couldn’t get him over there so they figured out a way to get him over here. I read an article where Walid Shoebat analyzed Routh’s appearance in photos and was very confident that Routh was a convert. I am familiar with things like the dark spot on the forehead from grinding the head on the ground in prayer and slippers with the heels pushed down. Shoebat called attention to the beard/no mustache look and explained it’s significance. That was a new one. IMO Routh is a convert. He could still have been ( & most likely was ) directed by others.
Routh being a Muslim convert isn't enough for explaining why Kyle was 'helping' him at a firing range. Perhaps Routh was an operative for those wanting Kyle dead and the only way they could get Routh with Kyle AND ARMED was to use a PTSD LIE to get them together at a firing range..