We just perceive it as such, and this should be fairly hard to argue against with all the scientific advances we have made up to this point, at least as long as you assume consciousness involves biology and physics at least somewhat.

Otherwise, you can't explain e.g. smooth perceptions of low FPS stimuli, delayed reaction times, and must ignore obvious limits on various biological and neurological rhythms, or other possible limits on continuity (e.g. quantum stuff) and rates generally.