Ultimately my opnion on this subject might be biased itself because i'm a guy.
But to people who want some examples of anti-male bias with which to analyze.
The lastest movies i could think of
Mulan (the 2020 version) and Wonder Woman 1984 (what a mess this movie is)
Anime might be too searing in this topic as it is know for being pandering for male audiences... A lot of shounen use villainess only on ocasion, most often they fall into the subservient category mentioned by op, and they often don't get punched square in the face like the guys do (thought it has happened)
What could be discussed is the overall presence of 'female powers'. powers that are generally less combat oriented being pushed on female characters for the sake of keeping them out of the fight. And how often these powers involve some for of manipulation or transformation.
Also maybe touch on how the guys get punched and launched, and break every bone in their bodies while fighting... But the girls get minor bruises and scratches before they fall down unconscious.
Funnily enough as i thought about this, i realized the efforts a lot anime are putting in pushing this away... Like boku no hero... Sure some of the girls powers are not as bombastic, but there are scenes that show them shining more than the guys who do have that.
However I still think the anti-male bias exists, is there... Like look at how the cast of villains has 1 woman, and her power is... Shapeshifting and manipulating people emotionally.
We could also look at stuff like... the entire horror Genre and how women have more tropes and roles there. And wether thats a good or bad thing.
A final point i'd like to make... Maybe the problem is not in the writer but the audience.
In the above examples... Mulan and Wonder Woman 1984 are 'girl power' movies, they serve to emphasize the woman against the male characters, and can often feel pandering towards women (just like guy power fantasies pander towards guys)
A lot of popular anime a made with a male audience in mind, that is simply how it is... And in general terms (not me) boys want to see girls being sexy and submissive so it makes sense for shounen and other shows to paint women like that... Because their primary audience will agree with them regardless of the overall opnion. Even if is a disgusting way to pertray women;
And the horror genre tends to be tied into eroticism , hence why a lot of the times there is a diference in gender between the protagonists and the thing chasing them, however this is the one i can talk about the least as i dislike horror.
So yeah... Maybe it's not on the writer, but on the readers... The writer write what he thinks people might want to read,