One of feminism's favorite sub-shaming tactics is the term "doormat".
By painting the submissive woman as nothing more than an object to be stepped on by anyone who walks by, feminism has so successfully characterized a submissive nature as a shameful show of weakness that I even heard hardcore BDSM submissives go out of their way to, quite unaccused, assure me that they aren't one, that they can stand up for themselves.
Blurring the line between submission and obedience may be the result of honest muttonheaded confusion, rather than tactical social engineering, on the part of feminists, but they couldn't have chosen a better tactic, both for their admitted goal of making women behave less submissively... and their apparent goal of making women disempowered and miserable.
But what is submission, if it is not obedience?
Well, obviously, obedience is doing what you are told to. Simple enough. And we all must be obedient sometimes, even the most alpha-male of us all. Don't obey your customers, your business goes under. Don't obey the custom of driving on the right side of the road, you're dead. And so on.
Certainly submissive people are often obedient. But this does not define submission.
According to Wikipedia,
Submission is the acknowledgement of the legitimacy of the power of one's superior or superiors.
but in a more broad sense, submission, whether to is to a superior with power, or to someone who does not have any real power over you, is treating someone else like a superior, or, to put it another way, treating someone else as if they were more important than you, whether they are or not.
The idea of treating others as more important may raise a few hackles, especially when we explicitly connect it to notions of femininity or womanhood. Suggesting that a woman, in particular, ought to be submissive will prompt some strong objections indeed, from some quarters.
But what is so important about being important? About being superior or equal in status? About not being seen as an inferior? The goal behind all of these things to be treated well. Being seen as important is not, in many cases, an end goal in itself, but a means by which people seek to improve their treatment by others.
And certainly a man is treated better if he is seen as important. Feminists often complain (complaining is submissive, but they don't notice that) that men who behave dominantly are respected, while women who behave that way are seen as cold and bitchy. While many of the women so complained for are actually cold and bitchy (they don't know how to do dominance), it may also be true that dominant behaviour in women just isn't rewarded in the same way.
Feminists would cry "injustice", but as usual, they fail to examine the other end of the scale. A man who behaves submissively is seen as weak, whiny, cowardly, impotent, or at least unimportant and therefore not worthy of good treatment. But what about a woman who behaves submissively?
When a woman acts submissive, even without being particularly obedient, people, especially men, like her... and want to treat her well.
The word "empowering" probably doesn't work here, given what we're talking about, but submission is one of the most effective tools a woman has for being treated well. It often seems that women are treated not according to how important they appear to be, but according to how well others like them. When a woman treats others as if they were superiors, they feel valued and appreciated and loved, and, if they are not defective people, they wish to return that feeling, and encourage that behaviour.
Being liked in this way is most useful indeed in building relationships, and, as I have stressed again and again, it is relationships, not achievements, that make women happy.
A woman who is deliberately submissive is pursuing her own highly effective strategy for being happy... one with the added bonus of making others happy as well. That's about as far from weakness as you can get.
If submission were obedience, this would be dangerous, of course. You can't just do what others tell you to if they haven't earned your trust. There are plenty of people out there willing to hurt or exploit you.
But when we understand that submission means treating others like superiors, it becomes very easy to understand how to submit without obeying.