With regards to Domestic Violence, many male advocate groups oppose approaching DV/IPV from a gendered lens because it's not effective. There have been numerous well-founded studies that show that most DV/IPV is bi-directional. Moreover, the power and control wheel (Duluth) model of IPV/DV is based on patriarchy theory has been found to poor characterize the dynamic in most abusive relationships. So many other things beyond misogyny that factor into abuse that stems from family history of abuse, trauma and addiction. The inventor of Duluth model, Ellen Pence acknowledges its failure:

"By determining that the need or desire for power was the motivating force behind battering, we created a conceptual framework that, in fact, did not fit the lived experience of many of the men and women we were working with. The DAIP staff [...] remained undaunted by the difference in our theory and the actual experiences of those we were working with [...] It was the cases themselves that created the chink in each of our theoretical suits of armor. Speaking for myself, I found that many of the men I interviewed did not seem to articulate a desire for power over their partner. Although I relentlessly took every opportunity to point out to men in the groups that they were so motivated and merely in denial, the fact that few men ever articulated such a desire went unnoticed by me and many of my coworkers. Eventually, we realized that we were finding what we had already predetermined to find."

So, from I've seen, male advocates object to a gendered characterization of abuse, not necessarily to dismiss women's suffering. It's to expose the weakness of the model. Moreover, male advocates object to the over simplified solution to the problem: “Men must do better.”