Can ffmpeg downsample pixels perfectly? I've tried all the swsflags options and figure the answer is no, but it can't hurt to ask just in case.  For example: downsample from 1920x1080 to 960x540, then upsample back to 1080 using the neighbor flag to recreate a perfect copy of the original 1080 image.  Neighbor comes very close but there seems to be some color shifting happening in the downsample.  Can another filter accomplish this, or is it simply the nature of the beast that downsampling will never be perfect?
That violates the rules of information theory. Look into the work of Claude Shannon if you wish to understand why what you are asking is mathematically impossible.