Why is my object rotation going back before rotating

I have obviously made a glaring error somewhere, but I cannot see it.

In the code below, I rotate a galaxy, which is a series of gameobjects in rings around a black hole. The code works except for one weird bug, the objects jump back by the rotation amount, before rotating the required amount back to their starting position.

I have tried many things including setting rotateAmount to 60f instead if -60f, but no joy.

Can you see what I am missing?

 void Update () {
     if (rotateGalaxy)
     {
         float rotateAmount = -60f;

         for (int i = 0; i <= (int)gameSize; i++)
         {
             galaxyRingTargetRotations.Add(galaxyRingTransforms[i].rotation *= Quaternion.AngleAxis(rotateAmount, Vector3.up));
             rotateAmount /= 2;
         }
         rotating = true;
     }

     if (rotating)
     {
         int j = (int)gameSize + 1;

         for (int i = 0; i <= (int)gameSize; i++)
         {
             galaxyRingTransforms[i].rotation = Quaternion.Lerp(galaxyRingTransforms[i].rotation, galaxyRingTargetRotations[i], (j) * smooth * Time.deltaTime);
             j--;
         }
         if(galaxyRingTransforms[0].rotation == galaxyRingTargetRotations[0]) 
        { 
              rotating = false; 
              rotateComplete = true; 
         }
     }

     if (rotateComplete)
     {
         Messenger.Broadcast("GetUsablesInRange");
         Messenger.Broadcast("GalaxyRotationComplete");
         rotateComplete = false;
     }
     rotateGalaxy = false;
 }