Fluid dynamics is largely about figuring out the relationship between forces. For a soap bubble sitting still, that’s primarily the effect of gravity, which makes the fluid in the soap film drain downward, and surface tension, which tries to maintain a spherical shape for the bubble.
Once you start spinning the bubble, though, there are new forces that come into play. One is the centrifugal force caused by the rotation, and another is the drag force between the rotating soap bubble and the air inside and outside of it. The addition of these forces drastically changes the bubble’s shape. It becomes wobbly and flattens out. Watch the contact line where the bubble meets the surface and you’ll also see it creeping outward toward the edge of the platform. (Image credit: C. Kalelkar and S. Paul, source)