The thing that you seem to miss though is that even if abuse was equivalent both ways, the need for emergency shelter is going to be far greater for women in our society due to the economic disparity between men and women.
Since men still typically out earn women their ability to secure a safe place to stay is far greater. THis is especially true when children are brought into the picture.
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"Teach a man to reason, and he'll think for a lifetime"
~P^2
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