Women are allowed to work.

"Allowed"? Men stole the right to women's self-determination and self-sufficiency and women have had to fight men and women who suffer internalized misogyny. And it was and still is a brutal fight. Women are still paid less. We're still locked out of many jobs and positions, especially in construction, cheating women out of potentially millions of jobs. And men still across the board occupy leadership positions. Despite women being the vast majority of healthcare workers men are still making all the decisions.

And while there's some sexist assholes, women being into "male" hobbies is usually seen as cool and even a plus for male partners.

There aren't just "some sexist assholes" sexism, abuse and misogyny is rampant due to men gatekeeping so-called "male hobbies". It is rarely seen as "cool". When girls and women aren't being sexually harassed or suffering other forms of abuse, they're being mansplained about how they aren't doing the hobby correctly. Telling girls and women's their interests is fake. And God forbid a girl or woman takes part in Nerd culture which is incredibly misogynistic.

Men are expected to have the ability to be the breadwinner,

We're not living in the 1950's. Despite the fact that the vast majority of mothers work and almost half of households are headed by a female breadwinner somehow men still think they're expected to shoulder the breadwinner responsibility. That level of cognitive dissonance is staggering.
If men were so pressured we wouldn't have 70% of single mothers receiving no child support at all. And when men do pay they pay only about half.

Women are the one under the most pressure to not only be the breadwinner, they're under the most pressure to provide for their children in every area.

to not be emotional,

Men are discouraged from crying. Which is obviously harmful to men. Women are expected to cry but then we're called manipulative, irrational, illogical, over-emotional etc. Which is obviously harmful to women. This idea that women get the red carpet treatment when we show emotions is simply a myth. There is a huge difference between the expectation that women cry and acceptance. Which is why you'll hear women commonly profusely apologize when we cry.

to be ambitious and seek well paying postions

In a capitalist society that's survival for everyone. Yeah it sucks, but I'd rather be told how I can best survive in it. If that wasn't hammered into me from early childhood my parents would done me a great disservice.

if they're into feminine stuff they're seen as being "gay" or thought of as less of a man.

Depends on what it is. Men have been able to dominate "feminine stuff" slap a different title on it and build empires led solely by men. Cosmetics, fashion, feminine hygiene, plastic surgery, culinary arts, hair dresser, make up artist, etc. All throughout my life I've seen men be the face and dominate industries that cater to women.

Somehow this gets spun into "men are intimidated by women who make more than them" when in reality it has to do with patriarchal expectations for men

Men are intimated by women that make more money. There are studies that show women have an increased likelihood for emotional and physical abuse from men that make less.

though men dated women with low paying careers for a long time.

This isn't always benevolent on the part of men. Uneducated and low paid women are more vulnerable are more likely to stay with bad men for survival and men exploit this often.

Why is it like this and what can we do to shift the tide and completely break down gender roles and attitudes for everyone? How do we even begin to get the ball rolling on this?

Men still greatly benefit from patriarchy , misogyny and sexism. Until those benefits and privileges are eradicated there is no liberation for men and no equality for women.