One of the mistakes people make when looking at the world and its messed up ways is to assume there is too much order. That natural Heirarchies and/or meritocracy is not Godly and a creation of the World system. Quite the opposite is true God is a God of Order and not chaos. Natural hierarchies based on God's ordering of Creation and society are good and not evil.
Egalitarianism is as Murray Rothbard said, " a revolt against God's nature." Women and men are different and have been made to be compliments to each other not the same. Some peope are naturally better at certain things than others. Some people are better leaders in endeavors than others. Others are better at helping people with leadership roles than being a leader themselves. Some roles were divinely meant for some and not others.For example; God's Creation Order goes God The Father, God the Son Christ, then man, then Woman and children. Man is the glory of God and woman is the Glory of Man. This does not in anyway condone abuse or other mistreating of women. However, they are to be submissive to their own Husband's and men are to love women as Christ loves His Church.
Women are forbidden by nature of being women from leading roles in Churches. No pastors, elders, deacons and no teaching men in the Church only the other women. Or working in the Nursery.
Complementarianism is part of God's Order of Creation and Egalitarianism is a direct threat to the Creation Ordinance set by God in The Holy Bible. Anything other than Equality Under The Law is a revolt against God Himself and not compatible with His Authority set down in Scripture.