Why do men and women sit on different sides in the church?
This is an ancient custom, which dates to the early Church.
St. Cyril of Jerusalem mentions in his lectures to catechumens:
Let men be with men, and women with women. For now I need the example of Noah’s ark: in which were Noah and his sons, and his wife and his sons’ wives. For though the ark was one, and the door was shut, yet had things been suitably arranged. If the Church is shut, and you are all inside, yet let there be a separation, men with men, and women with women : lest the pretext of salvation become an occasion of destruction. Even if there be a fair pretext for sitting near each other, let passions be put away. Further, let the men when sitting have a useful book; and let one read, and another listen: and if there be no book, let one pray, and another speak something useful. And again let the party of young women sit together in like manner, either singing or reading quietly, so that their lips speak, but others’ ears catch not the sound: for I suffer not a woman to speak in the Church. And let the married woman also follow the same example, and pray; and let her lips move, but her voice be unheard, that a Samuel may come, and your barren soul give birth to the salvation of God who has heard your prayer; for this is the interpretation of the name Samuel.