That's like focusing on a slow leak in a boat when there's a gaping hole taking in a ton of water.
Sure we can acknowledge both but that's actually the problem in its current form, the majority of what's acknowledged and addressed is women's struggles, while men are suffering more severely and at a higher lethality.
I get what you're trying to say but I see this same thing happen anytime the struggles of men get mentioned. It's that whole "well women have it difficult too" that sidelines the topic at hand.
Many women (not all) will do this all the time when they say things like: "Oh because men don't cheat on women" or "right, because men can't be toxic" and "so you're saying that men don't ..." etc.
It's a form of bringing the focus back to women (whom society currently considers to be the bigger victim who need to be protected at all cost, even if that means at the cost of men).