There are a lot of reasons. It’s just a matter of prudence. There’s an old Spanish saying “Entre santa y santo, pared de cal y canto.” (Thanks to L. for giving me the correct Spanish!) It means “Between a male saint and a female saint, a wall of brick and mortar.” Of course, that’s an exaggeration, but the point is that you’ve got normal people who are trying to be faithful to a life of celibacy. Too much contact between them can lead to all sorts of moral dangers and scandal.
Yet there’s another good reason: Men and women are simply very different. The purpose of Opus Dei is to give spiritual direction and other means of spiritual formation. When a priest preaches a meditation to a group of men he’s likely to say things in a different way than he would to a group of women. He’ll emphasize different points. He’ll use different words. He’ll use different examples and different humor. The women who give spiritual formation to the women in Opus Dei are much more likely to understand a woman’s point of view and her struggles than a man would, and vice-versa.
This view may not be popular today in a world that tries to pretend that the differences between women and men are merely physical, but psychology and psychiatry are continually affirming these differences. In my opinion, St. Josemaría, was truly wise in this matter.