I am not a man myself, but I do think feminine men are cool. However, I have noticed a disturbing tendency in the media. Men who do not conform to stereotypical masculinity are rarely portrayed in a positive light. In many cases, they are outright vilified.
The more overtly a male character’s stereotypically feminine qualities are, the more likely they are to be depicted as evil. The anime Inuyasha contained multiple examples of this. There’s Naraku, a feminine-presenting man who is the source of almost every main character’s suffering. The same series also has Sesshomaru, a feminine man who is cold-hearted and ruthless (though to be fair he goes from villain to antihero as the story goes on). The series has others as well, but those are the most prominent. The Final Fantasy games had multiple such villains, such as Sephiroth and Seymour Guado (both of which had evil plans that involved destroying the world). Really, there’s more examples of this than I could describe in this post.
There is one such character however, that warrants special mention: Griffith from Berserk. The story goes out of its way to highlight his femininity, describing his appearance in feminine terms and how strange it supposedly is that he both has those qualities and is a man. He is also a profoundly selfish, manipulative, and ruthless person. He enslaves the protagonist (who he later tries to kill), treats everyone like a means to an end when they aren’t an outright enemy, sacrificed all of his loyal followers to evil cosmic beings in order to become one, and also did some things I’d rather not go into detail about. One thing worth mentioning is that he is contrasted with the hypermasculine protagonist Guts, who we are expected to sympathize with.
Narrow gender expectations hurt people of all genders. In the case of narrow understandings of masculinity, it tells men that they have to fit a narrow mold in order to be seen as “real men.” Many of the problems inherent to patriarchy are reinforced by such things. The media should challenge gender norms, not demonize those who don’t conform to them.