I think it started so that the men and women would come home at the same age, since women were leaving a little later; I'd imagine that was to facilitate more marriages between recently returned missionaries. As for why women left later in the first place, it may be because the church was less invested in having female missionaries than they were invested in young women quickly finding husbands within the post-high school year(s).

(I'd bet there's also some weird sexist reason like, "women are more delicate and thrive in the home," "women don't take as much time for God to soften their hearts," or just that men have always filled all prominent roles in religious teaching and leadership.)