The analysis I've seen, mostly from men who study this and who are trying to help create a better culture, is that we are far better off appealing to men's self interest in reducing patriarchal norms that harm them as well than in trying to appeal to a sense of civil rights or humanity. Without shifting patriarchal Man Box messaging, we're fighting against a constant headwind where many men double down on their entitlement and right to dominate and control women rather than do the "feminine" work of introspection. As Mark Greene notes,

"For men raised in our bullying dominance-based culture of masculinity, self reflection is forbidden, punished. Who we authentically are doesn’t matter in Man Box culture. We are trained instead to model our identity on a narrow set of rules for how to be a man. The rules of Man Box culture.

Don’t show your emotions.

Be tough, never ask for help.

Be heterosexual.

Never talk about anything deep.

Be a breadwinner not a caregiver.

Have control of women and girls.

Have lots of sex.

All these rules require we show dominance over those around us, expecially over the women in our lives.

Living by the generations-old rules of the Man Box means asserting dominance in little and big ways in every interaction. Our response to pushback? Double down on bullying, etc."

https://medium.com/@remakingmanhood/the-gop-has-weaponized-the-man-box-f498a7594700

Jackson Katz teaches men how to stand up for women and others as a leadership quality, making it more palatable by masculinizing it, but this needs to become much more widespread if it's truly going to have an effect.