I have a slightly different take - our current ML models try to approximate the real world assuming that the function is continuous. However in reality, the function is not continuous and approximation breaks in unpredictable ways. I think that “unpredictable” part is the bigger issue than just “breaks”. (Most) Humans use “common sense” to handle cases when model doesn’t match reality. But AI doesn’t have “common sense” and it is dumb because of it.
I would put it in terms of continuity of state rather than continuity of function: we use our current ML models to approximate the real world by assuming that state is irrelevant. However in reality, objects exist continuously and failure to capture ("understand") that fact breaks the model in unpredictable ways. For example, if you show a three-year old a movie of a marine crawling under a cardboard box, and when the marine is fully hidden ask where the marine is, you will likely get a correct answer. That is because real intelligence has a natural understanding of the continuity of state (of existence). AI has only just started to understand "object", but I doubt it has a correct grasp of "state", let alone understands time continuity.
