What general media does this? Can you cite examples that don't consist of trolls online? Keep in mind that American media is largely Right Wing outside of certain spaces like MSNBC.
I see some people talking about this "powerful feminist lobby" holding young men back from success in life yet I don't really see it being manifested outside of certain women being shytty online trolls.
The decline of fatherhood and offline socialization plays a much bigger role in this than whatever "general media" you're referring to.
Modern Disney is an easy example. Hollywood is by and large decidedly liberal. IDK how you can say American Media is right wing as a whole when outside of the Murdoch sphere of influence right wing media is largely censored for good reasons.
The media is more explicitly pro female and only implicitly anti male at most usually. They'll signal boost feminist or gay shyt and vilify male centric stuff or quietly deplatform it and people notice. Nobody can call it out without being accused of being misogyny so it creates this dynamic where shyt bubbles on the fringe.
This disingenuous manner of discourse is what gives the Andrew Tate types a lane tbh. People can see the bs & sleight of hand which enables the grifters to market themselves & their beliefs as forbidden fruit on some "WHAT THEY DON'T WANT YOU TO KNOW". People trying to constantly deplatform Joe Rogan's podcast pushed it's popularity over the top. I've never seen any Andrew Tate shyt on my social media until he began getting deplatformed, then suddenly you start seeing people posting "reaction videos" of his content with some person on the other half of the screen nodding along.
The approach taken in the last decade has been wrong, we're seeing that now. Further villifying men or going about these 90's Christian Group censorship methods only makes alt right content frame itself as rebellious & cool.
Anybody who knows real men in their lives can see the Andrew Tate types as the weirdos and frauds they are. But when media and pop culture push to sissyify men to such an extent, the bar becomes low enough for an Andrew Tate to step over.
Overall this is another hard pendulum swing in the opposite direction much like MAGA as a backlash to the Obama era