If there had been a massive migration of hundreds of thousands of people, and even more so hundreds of thousands of slaves, from late bronze age Egypt (a powerful, old, highly literate kingdom), we would expect to find significant evidence of this (inscriptions, local stories, migration sites, etc). The absence of any such evidence, while not conclusive proof of course, constitutes evidence against this event happening.

We also know for example that the types of beliefs detailed in Exodus, especially the idea that the Israelites worshiped Yahweh alone as the only God, are not historical. Belief and worship of other gods were common in both the ancient kingdoms of Israel and Judah long after the supposed time that the Exodus happened - in particular El (who was later associated with Yahweh) and Asherah (who was sometimes seen as the wife of Yahweh). So at least this aspect of the Exodus narrative is directly contradicted by archaeological evidence.

This is similar to the reason we believe the stories in Genesis are not historical, e.g. the flood, - if they had been historical, we expect that they would have left behind certain marks; those marks haven't been found, so we have a reason to believe that they didn't happen.

We know the Exodus didn't happen because the supernatural elements described cannot have happened, and there is no evidence of any such mass migration in the archeological record, nor any non-Biblical references to such an event taking place.

It may be the case that the Exodus tale is a recontexualization of various historical memories of nomadic resettlement combined with political narrative, but the actual story as described in the actual Bible didn't happen.