Because unlike too many Christians, I don't think believing the Bible is an "all-or-nothing" scenario.
Besides, who said I believe them? I don't -- not 100%, anyway. As Reagan said: "trust, but verify."
Furthermore, I know that if the old writings were going to lie, they'd be far more likely to lie in order to put themselves in a more favorable light, as opposed to unfavorable. So even if I believed that the Egyptians somehow managed to expunge every single reference in their own history to the entire period of the Hebrews' captivity and subsequent escape, their rivals and enemies would have no reason to do so. If anything, they'd be more inclined to exaggerate the claims far beyond anything the Hebrews wrote.
They did not do this. They wrote about nothing. Their enemies were laid low by their own slaves in spectacular, empire-crumbling fashion, and nobody who had the most to gain from it so much as mentioned it.
That doesn't strike you as the least bit odd?