Possibly something cultural? That you'd try to be polite in this situation:

I've had this American friend who I used to talk with/hang out with before our (school) work has gotten busy since last year.

Still we would manage to hang out once in while.

I just noticed this friend seems to complain a lot about not being able to talk/hang out as much. But I'm the one who would always schedule a time, place and stuff. I mean, I'm the one who would initiate gathering, what this friend did was in the end saying "this is fun, we should do it again/more often." However I'd never heard from the friend again until I ask when the next gathering could be.

The complaint I received seems to suggest I should organize things more often? Or should I take it as a way to say not to hang out as much(?)

How would you interpret it when your friend seems eager to hang out with you but never initiates it until you do? Still, they'd complain about not hanging out much (I just feel "we should hang out more" here is being polite?)