No, it doesn’t!
YES, He expects MEN to be the head of the house, but that doesn’t mean women are their slaves.
Ephesians 5:24-29 is actually a beautiful explanation of how our earthly relationships should reflect our relationship with YHWH/Yeshua! Read in context, we see that Yahweh (YHWH) views men and women as equals, yet each with their own, specific gender roles:
Ephesians 5:24. And as the assembly is subject to the Mashiyach, so also let wives be to their husbands in all things. 25. Husbands, love your wives, even as the Mashiyach loved his assembly and delivered himself up for it; 26. That he might sanctify it and cleanse it by the washing of water and by the Word; 27. And might constitute it a glorious assembly for himself, in which is no stain and no wrinkle and nothing like them; but that it might be Set Apart and without blemish. 28. It is fitting for men so to love their wives as (they do) their own bodies. For he that loves his wife loves himself. 29. For no one ever hated his own body; but nourishes it and provides for it, even as the Mashiyach (did for) the assembly. (AENT)
 Many put emphasis on "who" has authority but Shaul always makes a pretext of loving one another as well as submitting to one another before describing the spiritual order of men and women.
 These verses have been twisted by Christian theologians to dish out a “limited atonement” theology that only Christians “get saved.” They tend to forget that our Messiah’s suffering established atonement for all of YHWH’s people, from the time of Adam, millennia before “Christianity” even existed.
They also tend to overlook the fact that the original Netzarim faith (which is clearly spurned by the Church) is being referenced; NOT the “modernized, grace-only” Christianity. If Paul were to witness the rampant paganism in the modern Church, he would never endorse it or be part of it.
Yeshua says to all who break Torah, “I never knew you, depart from me ye workers of iniquity.” The “glorious assembly” he suffered for consists of those who live FOR and IN Messiah Yeshua, who are sanctified by the Word of YHWH, and whose love for YHWH and each other is based in Torah rather than on the doctrines of men.