You're confusing parallax for rotation. Set something on your counter, and take a picture of it with your phone. If you walk four feet to the left, and take another picture, it will be at a different angle of parallax. That sort of transition would be impossible (or at least, incredibly small) given the nebula's great distance to us.

On the other hand, stand in one spot, and turn your phone on its side and snap another shot instead. Now you haven't moved relative to the object all, but your image is rotated.