Anti-shake measures in the lens move a segment of the optics in order to balance against your natural body vibrations when holding the lens. This takes a few moments to actually start moving, detect the motion and then adjust performance to match vibrations. Therefore if you're the type of person who points and shoots very fast at a subject; then the anti-shake can actually cause blurring in the photo because its not yet got up to speed.
Depending how you shoot sometimes it can help to turn it off if you are going to shoot like the above. It's also good to turn it off if your shutter speed is fast enough to counter handshake anyway. Note that with very long lenses like the 600mm you've got, I've actually found having it on helps steady the viewfinder image when keeping focus tracking a subject. So that can be a boon even if your shutter speed is already fast enough to overcome handshake blur.