Most Helpful Girl
The reason is no different from why men get into relationships with such women or why some people, in general, befriend people who are inferior and subservient to them.
Both the surface reason and the root cause are noted in your post, lol.
On the surface, it's because these people feel the need to assert control. People who are clingy, needy, insecure, dependent, and passive are easier to control. Such people make it easier for the controlling person to appease their own need to validate their ability of asserting control. They serve as proof-providers to the controller that he/she has control over his/her life. If you can dominate another individual, that provides you with direct evidence that you've got things under control.
That brings me to the root cause: insecurity. People who have such a dire need to prove to themselves that they're in control, to the point where they seek out subordinate, submissive lovers, are people who actually lack security in their ability to assert control. If they were secure, they wouldn't seek out individuals that they perceive to be beneath them. They'd seek out individuals who are roughly equal to them in their self-perceived rank.
(I should also note that seeking out someone who is domineering and/or above your rank also has insecurity as its root cause, but that's a different matter)
Most Helpful Guy
Part of it is to prove something that they can manipulate someone that society has deemed the dominant sex. However, in the natural state, women like men who take control; this, these relationships do not last. The domineering woman will move on because it gets boring.