At first glance, it looked to me like part of the issue is that the combination of image size, frame rate, and rotation speed is such that the boxes on the periphery are moving by more than their own size between each frame.

I tested it by marking one square on its course through the animation. It's only a bit over 1/2 of the way out from the center, but there are spots where its position in one frame does not overlap with its position in the other frame. It was actually very hard for me to keep track of the square I was marking as I was stepping through the GIF one frame at a time; there was a fair bit of guess-and-check work.

Anyway, marking one box definitely weakened the illusion, and I suspect that decreasing the amount of rotation between frames by about 70% would make it go away entirely.

Unfortunately the filesize is nearly 1MB and there's nowhere I can upload an image that large to share it (nor can I decrease the resolution without 'breaking' it), so y'all will have to trust me on this.