clearheaded:
I believe you are confusing me with another poster, as in none of my comments on this thread have I brought up the “chefetz” (or “object”) issue.
As far as the “equality” issue, the sources I quoted above, as well as previous comments I posted here, clearly indicate otherwise. Just as an orange isn’t “equal” to an apple (or better than an apple), men aren’t “equal” to women (or better than women.) So no, men and women are not equal.
As far as the husbands “ruling” their wives, as brought from the Torah – Chumash Bereishis [and the cited meforshim above] is concerned, this is nothing to be ashamed of. Is one ashamed that the King of his country is his ruler? No, such is the natural state of affairs. Same as between husband and wife.