Speaking for myself only, I can't say I notice everyone else's problems. I wouldn't limit that to issues of misogyny though..
I never know how to comment on this stuff where I can't personally relate to the sentiment (feeling threatened by the accomplishments of others). The only point I wanted to distinguish with respect to Hannity is that he leverages negative sentiment for ratings. If he couldn't get ratings from his nonsense rant about Jill Biden, he would just move onto something else. That's what pundits do, at least in the US.
When looking at stuff such as language, culture, gender, ethnicity, society, social class, - and when looking at how a particular society (and political culture) chooses to define itself and to describe itself - it is very instructive to see what is insulted in that culture and to try to ask yourself why.
Men tend to be insulted as individuals, whereas for groups who are less powerful, because they are less powerful (and the dominant group - yes, middle class & upper class white males, preferably heterosexual in orientation) and because the more powerful define themselves in terms of who they are not, insults are directed at these groups, as group slurs or insults. The mere fact of being born in, or belonging to, one of these lesser groups is what lies at the core of the insult, (and belief that they are - by definition - lesser, inferior and should be subordinate).
Now, the precise form such inuits (and beliefs) take depends on the particular society.
In the UK, for example, some of the nastiest and most offensive stuff is aimed at, directed at, targeted at, at social class, which is a more salient division in that society than is ethnicity, or race (though the latter most certainly exists, - female and male MPs who are black have been stopped by the police "because you couldn't be driving that kind of car", black barristers have been treated as though they were the defendant by both court officers and the police and so on, ad nauseam) - although when both intersect, or collide, the results are positively putrid, whereas in the US, race is the original political sin that has beset the sense of identity and sense of self worth of the state since the Founding Fathers thought that Enlightenment values should have political expression over two centuries ago.
However, re gender, the very fact of being a woman - "throwing like a girl", where the simple fact of being "like a girl" is the insult - is deemed an insult to a man, especially a man who defines himself strongly in terms of gender, and - to be perfectly candid - this tendency seems to be a lot more pronounced in the US, where women who decline to mask their intelligence, or hide their educational credentials - especially if they come from lower class backgrounds, or are women of colour - are seen as a threat by some men.
I recall not just the awful election of 2016 (and, while Secretary Clinton did indeed carry some hefty baggage, the mere fact of her gender gave rise to a degree of misogyny I have yet to see in western Europe, and while there were many reasons which meant that she failed to gain election, the fact of her gender, and the misogyny that gave rise to, was undoubtedly one of them), but also, the inchoate the rage, two decades earlier, when then Hillary Rodham - a successful lawyer in her own right - expressed doubts about taking her husband's surname, as she wished to be known by her own name.
Moreover, I recall the incredibly vicious venom with which Michelle Obama - a formidable, exceptionally intelligent, and supremely well qualified individual, someone of dignity, grace, and sheer class - a threatening fusion of ethnicity and gender to many of those who dwell on the right - was described by right wing commentators when she lived in the White House.
And I can effortlessly predict without seeking recourse to astrology or being compelled to burn animal entrails, the serious cardiac arrests and perfervid frothing reactions from Republicans if ill-health claims Mr Biden while in office, and leads to Vice-President-Elect Kamala Harris being sworn in as President Harris.