For example: Ephesians 6 goes on from what you clipped: 25 For husbands, this means love your wives, just as Christ loved the church. He gave up his life for her 26 to make her holy and clean, washed by the cleansing of God’s word. 27 He did this to present her to himself as a glorious church without a spot or wrinkle or any other blemish. Instead, she will be holy and without fault. 28 In the same way, husbands ought to love their wives as they love their own bodies. For a man who loves his wife actually shows love for himself. 29 No one hates his own body but feeds and cares for it, just as Christ cares for the church. 30 And we are members of his body.
This seems to me to indicate that husbands should be self-sacrificing and putting their wives' needs above their own. All the submission indicated here is similar to the way that Christ (the Son) submits to God the Father. These would have been very strong and shocking words in that culture, that normally would have allowed for husbands to have complete "rule" over their wives, and instead is urging husbands to self-sacrifice for their wives. So if anything, it would have been improving the standing of women rather than "keeping them down."
If you're married, have you ever willingly given up on your own desires, instead following your spouse's needs/wants? Have they ever done the same for you? This seems to be what this passage is encouraging.