Firstly, I doubt that its ever an entirely free choice on either side --- and I'm sure many readers with experiences in this field will have views here. And of course, women abuse men, far more than most people recognize, as well.
Abusers tend to both pay excessive attention to their own emotions and feelings, and little or none to the emotions and feelings of their target, and they are often people with a shaky sense of self-esteem who feel boosted by putting someone else down. Also, they can be inarticulate, especially emotionally, and to it out either physically or verbally when they can't cope with emotional challenges, either from their victim or from other aspects of their lives.
And we wish we knew why women, especially, stay with an abusive partner. Part of it seems to be that having been browbeaten into a low sense of self-worth they find it hard to be independent and asserttive enough to recognize really that they deserve to be treated properly, and partly they can harbour a delusion that "he will change". even that they will manage to change him.