Using church language then.
Authority - this is a very common term in the church. Priesthood leaders have authority. That authority applies to women, but never the other way around. Men administer ordinances to women, but not the other way around. Men have authority to call women to serve in callings, but not the other way around. There are a million more examples.
Most importantly, men have authority to discipline women, but never the other way around. There is not circumstance where a woman would sit in judgment over a man and decide on church discipline. But if a woman's worthiness is called into question, a man, or group of men, have authority to decide whether to issue discipline. They can excommunicate her. But never the other way around.
Preside - this is another common term in the church. You say you don't have any power or authority over any woman, but you actually do. The family proc flat out says that you are supposed to preside in your home. If "presiding" isn't a form of "power" or "authority," then I guess pick a different word. But it sounds like power and authority to me.
For real though, I honestly don't get the dispute over this. If someone wants to argue that it's God's will, I'm open to that. But the suggestion that men and women are on equal footing in the church is just crazy. It's so completely obvious. It's across the entire structure of the church.