Most objects in the universe cycle around their centre of mass: earth, sun, galaxies. Even galaxy clusters.
However, the whole universe doesn't possess an angular momentum. It can't: If it had one, the centre would be a special point (which isn't allowed) and the velocities of the outer regions would easily become infinite.
How does the angular momentum vanish with increasing scale?
Shouldn't the laws of nature that lead to cycling for smaller objects also hold for larger objects?