Show, don't tell.
I get that it sounds trite and unhelpful given how common the advice is, but in this case it's true. The way you get such a message across is to show it in the context of your narrative rather than having one or more characters act as mouthpieces.
- Show a male character who is a father and show that they can be as nurturing and loving to the child as the mother
- Show a man being abused by their spouse and have other characters react with the same appropriate horror they would for the reverse, rather than denigrating him for "letting a woman take advantage of him" or outright not caring about his situation or believing he could be abused.
- Show a man who like non-traditional masculine things, but then show his way of life as just as valid as a more stereotypical guy.
The best way to do it is always remember that this is supposed to be a theme of your work, it's not supposed to be the only thing your work is about. This is why a lot of pro-feminist works like Wonder Woman and Avatar: The Last Airbender are remembered so fondly, they have more to say than just a feminist theme. At the same time, looking at well-done examples of feminist literature and applying them in the same way is a good idea.
But the big thing is don't make your work anti-female in order to convey this message. This is a big problem you see in a lot of supposedly pro-feminist pieces today like Captain Marvel or the Charlie's Angels remake (hence why I said, "well-done"), in which in the process of trying to elevate women the movies often make men look like incapable idiots who can't do anything at best or "rapebeasts" at the worst. In your context, it would be "avoid portraying women as vicious harpies who hate all men". You should work to have your female characters be as complex and interesting as your male ones (unless the setting is one where the cast is expected to be all male like a foxhole in World War I), even if they aren't as much of a focus.
The way I've heard it say is that if you are trying to write a pro-X piece and can't get people both from group X and not from group X to stand up and applaud at the end, you're doing something wrong. Writing like this isn't just about catering to group X, it's about expanding empathy for people who aren't in that group and breaking stereotypes.