That is 100% perfectly normal, it is just the FC trying to compensate for the quads changing orientations as you wiggle it. Also, the quad has no way of knowing the props are on or not, so how could it possibly be what keeps it from arming?
If it won't take off, what does it do, does it flip out? Looks like the motors are spinning in a coordinated way, so I'd check the flight controller orientation and the motor order first.