The statement that there are no battered women is, of course, absurd. However the suggestion that men and women don't, "...beat each other up", is almost equally absurd, as is any attempt to suggest that women are always passive victims when domestic violence occurs. The mutual nature of domestic violence is well documented. Researchers Richard Gelles, Murray Straus and Susan Steinmetz have confirmed it repeatedly.
Also, Cal State Long Beach professor Martin Fiebert summarized 111 different studies with over 77,000 respondents and reported that women initiated domestic violence nearly as often as men.
http://www.csulb.edu/~mfiebert/assault.htm
Professor John Archer of the University of Central Lancashire analysed 17 international studies published over the last 20 years. He reports that although women are more likely to be injured as a result of domestic violence, men were equally likely to be victims of less violent forms of abuse, which constitute the overwhelming majority of cases.
(John Archer. Sex Differences in Aggression between Heterosexual Partners: A Meta-Analytic Review. Psychological Bulletin Vol. 126, pp. 651-680, 2000)
And according to the U.S. Department of Justice it is women who are the perpetrators in the majority of cases of child abuse, and parental murder, arguably the most severe forms of domestic violence. Mothers commit more than 60 percent of confirmed cases of child abuse and 65 percent of parental murders of children.
http://www.acf.dhhs.gov/programs/cb/publications/ncands97/s7.htm
Also, I see that when people debate here, they often point to other positions their opponent has taken in the past that they claim have been shown to be wrong. They suggest that this is evidence that he must be wrong this time too. It's no such thing.