The reason for this has to do with the flow of the Nile River.
Because we live in the Northern Hemisphere, we tend to think of north as “up” and south as “down.” But there is really no logic behind that. There is no reason that north should be thought of as “up.” If we looked at it logically, there is no reason to feel that “Lower Egypt” ought to be in the south and “Upper Egypt” in the north.
The terms “Upper Egypt” and “Lower Egypt” do not derive from where they are on a map that has north at the top. Instead, they are derived from how the Nile River flows. When we talk about rivers, “up” is upstream, nearer to the source of the river. “Down” is downstream, farther away from the source. The Nile River flows from south to north. Therefore, the upper Nile is south of the lower Nile. Upper and Lower Egypt were named because they were on the upper and lower Nile, respectively.
So, Upper Egypt is south of Lower Egypt because the upper Nile is south of the lower Nile.