Shounen is a genre (which I had to search to learn what it is just now), not a justification.

It sounds like there is a circular justification you have seen some people using.

Much Western media is also full of sexism. It’s just not quite as obvious as it used to be.

The only validity to the argument that “it’s Shounen” is that when you remove the sexism from sexist material, it feels different, because it is.

The “targeted toward men y’know” part is both circular and also written from an assumption that things “targeted towards men” would necessarily be sexist, which is a subtle (and perhaps unthinking) but huge disservice to men. More accurate might be “it’s targeted towards and responsible for reinforcing certain sexist undeveloped male mindsets and appetites”.

“What I don’t understand is that why are they doing that?”
They’re writers with a job working for a company which is targeting a perceived market with a recorded sales history, by generating more content within a genre.

“Do the writers have strong conviction that male readers/audiences feel pleased by showing them the images that men are more superior than women?”
Perhaps but not necessarily. No more than Stan Lee believed in fighting crime as a costumed vigilante in real life. Each writer will be a person with their own mindset. It’s only necessary to understand and use that pattern to write more of a genre.

“Would it damage men’s ego if women are shown to be just as competent as men?”
No. And if someone has a fragile ego-identity that depends on such things, they’re not particularly deserving of the adult label “men”, and they’ll be better off having that notion challenged in any case.

“Have they not noticed the gender-equality movement and its impact to readers of both gender?”
Again, the writers aren’t choosing to churn out Shounen as an expression of philosophical truth about society. They’re getting paid by a company which pays for Shounen because they have high confidence they can keep selling that genre as a product.

So the writers might or might not know about gender-equality movements or social impacts. If any of them do decide it’s not what they want to write, then I suppose they either regretfully do it anyway or choose not to, and are thus no longer the subject of the question.

“Why won’t they bring a wind of change?”
Perhaps some Shounen writers have reflected and started writing something else, but then they’re no longer Shounen writers. I imagine amongst the countless works of anime and former anime creators there is some less sexist stuff.

Shounen is a Japanese product, and Japanese society isn’t best known for its kindness toward women. Japan also isn’t receptive to culture change.

Moreover, the Japanese society is now facing a problem of the increase in shut-in. They are men who refuse to socialize because of pressure to be a “real man” society impose on them. As a result they prefer to stay at home and fantasize about a world where they are successful and women are crazy about them. Manga writers are preying on this fantasy by creating stories with strong male characters and weak women for them to rescue and own. They know as long as they keep pandering this fantasy, they will get money.

I can’t comment on the Western anime fans going along with this trend though.