Cogito, don't be daft. That is very odd thinking!
I've been trying to think of an example of where DH and I have disagreed to give as an example. Really it is just caring for the other and their opinion. If DH and I were debating over the sofa discussion (assuming these are identical sofas, both fit in the room etc - we're just deciding colour), it wouldn't be someone forcing their decision on the other. Perhaps it would go:
Me: I really think the blue is better. With DS, it will hide the stains better.
DH: I prefer the red. It goes better in the room with the chair.
Me: Well, we need to decide one or the other.
DH: Okay then, shall we go for blue? I know you care more about these things than I do.
Me: Are you sure? Thanks, great. We'll have the blue. Perhaps we will get the cushions in red.
(Gosh, wasn't that banal?!)
Then when it comes home, when I realise that red would have gone better, I shouldn't start saying, "Well, you should have stuck with blue. This is your fault," and DH shouldn't say, "I told you so."
It is a decision that we have agreed upon, caring about the other's opinion. It doesn't mean that we have to ignore our own.
I think garlic puts it nicely when she says, "You get this semantic discussion a lot on christian forums, Cogito. The ideal is, I think, that both partners give up their superego in favour of being a couple. The "submission" is a defeat of selfishness, not of the whole personality."
I'd disagree with "The fact that the man has to be the default winner, in cases of dispute, gets up my nose immensely. In practice, when a couple really can manage a relationship this well, they quickly learn that each partner has their own areas of wisdom so the other should 'submit' to their expertise."
Of course we have our own areas of expertise and that is recognised in how we work out our marriage and decision making. I am a doctor and a scientist. I know about that sort of stuff. I am also much better at interior design and cooking than DH (so really I would just make the sofa decision unless he really hated it). I make those decisions. DH is a geek - he makes all the technology decisions in the house, but he will listen to me and take my thoughts into consideration about what (say) computer to get.
(The only difference to that is whether DS needs to go to a doctor. I am also cautious that doctors can fall into the trap of being too complacent or too nervous about their own children, so DH tends to make the decision about whether we need to take DS to the doctor as the more 'normal' parent!)
DH is not the "default winner". That shows that you have to have a winner, rather than the caring mutual submission of putting the other first so that the couple or family is the winner.
Cogito is right though when she says, "If no-one submits walking through the doorway, both try to go through together and get stuck..." Of course, that is why submission in marriage (in any relationship to some extent) is important. There has to be some way of deciding what happens. This isn't about "winning" though.