There are many layers of symbolism and intentionality to woman coming from the side of man. Christ, as the new Adam, pours out from his side blood and water thus birthing the Church. Mary, his mother is the new eve on the order of grace. She is woman who brings new life and is the ark of the new covenant.
The Church is thus decidedly feminine in its relation to God.
Using rib in English can obscure the intentional continuity between the stories and concepts. But I don't think it's necessarily a slight. Using rib has its own benefits in expressing the physical nature and like being of man and woman.
It's far more revealing to take these things at face value rather than to assign ideological cynicism.