Angular velocity is the angle swept out per unit time, rather than a distance per unit time. It does not cancel, as both "sides" of the object are travelling the the same angular direction, even as they travel in opposite rectilinear directions.
Yes there is motion, as I said something spinning, spins. But it spins in relation to something. To what is the angle measured? It is external to the object in question. The whole point of this exercise is to determine why something would spin. I am essentially saying that the impetus is external to the body. IOW gravitational forces directed towards a central point is not enough to impart angular momentum to the body in question. I believe it must come from something external to the mentioned body.