Why are there separate doors for the es in Flatland?

In the Edwin Abbott novella Flatland, there are separate doors for men and women. This has something to do with men being polygons and women being line segments, but the specifics are hard to find online. It is mentioned that it is very easy for a woman to impale a man (she's a line segment; therefore, she has sharp ends), but I don't understand why a woman couldn't simply step through a "men's" door sideways.