That's the common belief. How do we know it's true, and not a "just so" story?
My investigations into this led me to CDC reports (and others) showing that DV / IPV was largely 50/50. Harm was more often done to the smaller partner (i.e. women). But women also tended to use more weapons in their attacks.
These reports aren't hard to find. Most people don't look.
In particular, from the key findings sections of the report from the National Violence Against Women Survey:
"Women experience more intimate partner violence than do men: 22.1 percent of sur- veyed women, compared with 7.4 percent of surveyed men, reported they were physi- cally assaulted by a current or former spouse, cohabiting partner, boyfriend or girlfriend, or date in their lifetime; 1.3 per- cent of surveyed women and 0.9 percent of surveyed men reported experiencing such violence in the previous 12 months. Ap- proximately 1.3 million women and 835,000 men are physically assaulted by an intimate partner annually in the United States." [1]
[1] https://www.ncjrs.gov/pdffiles1/nij/183781.pdf, page 6 under Key Findings
Further, women are more likely to be murdered by their partners than men. Safe Horizon's has a basic fact sheet that is pulled from sources at the bottom of the page: http://www.safehorizon.org/index/what-we-do-2/domestic-viole...
http://www.sp2.upenn.edu/ortner/docs/sorenson_doc2.pdf
Each year, more than one million people in the United States obtain restraining orders for intimate partner rape, physical assault, or stalking (Tjaden & Thoennes, 2000). An estimated 18.9% of the more than 5 million U.S. women and 4.3% of the more than 3 million U.S. men who are physically abused, raped, or stalked by an intimate partner each year seek and are granted a restraining order.
Whether or not that is the case, it is also possible that it is more that when they are (or, in the case of murder, expect to be) the victims of such things, they feel they don't have other effective remedies outside the legal system, whereas men feel more able to respond effectively (whether or not legally) with physical violence.
So these things to some extent perpetuate eachother.
Perhaps the reason why women seek TROs and ROs is because they are much more likely then men to be the victim of physical assault, stalking, harassment, or murder from their partners or former partners.