Seems like there are a lot of social factors and systemic issues at play.
Men are still assumed to be the main breadwinner and when children come along, I think there's motivation to work the long hours needed to progress up the career ladder instead of being encouraged to take shared parental leave or part-time work. As mentioned by a previous poster, most jobs and office roles are historically based around an all-male working environment. It's quite probable that employers are more sympathetic to male employees being promoted because 'they now have a family to support'. I wouldn't underestimate the entrenched gendered roles of men providing for the family while women do the nurturing and therefore their career is seen as 'less important'.
Women end up taking on more part-time and flexible work so it fits around childcare. There are women who don't mind this and enjoy the opportunity to focus on children more and career less. Other women might be frustrated. Either way, it will translate into lower pensions or overall spending power as the years go by.
I haven't looked too much into this topic, but like many systemic issues it's not something that is solved easily or quickly.
Good quality state subsidised childcare is important. Having roles that are open to more flexible work and less about slogging long hours will make such jobs more parent friendly, especially for women.
I don't really hear this being said, but I think it would be a really good mechanism for bridging some of the pay gap - motherhood and childrearing should be valued as an important role in itself and a contribution to the economy. I would support a government scheme that pays mothers for their job of giving birth and looking after children. Not every woman desires to be a manager or company director and many women derive great joy from focusing on family instead of wanting to play the career game. Motherhood shouldn't be an unpaid role. It's important work. If we hired a person to do all the tasks involved in a mother's role, it would command a hefty pay. The societal expectation that women should do this for free needs to change.
It should be treated as a proper income, so taxed appropriately and ensure a proportion goes towards a future pension etc.
I personally don't think it's productive to compare different jobs and try to draw some connection between them in terms of pay. It's more important to elevate the importance of motherhood and realise its contribution to the overall economy and look at ways to ensure mothers are paid for this role.
Regarding debates with partners - you don't change someone's mind overnight or by accusing them of being sexist / misogynistic while insisting your own position is the only correct and flawless interpretation. Both people will be approaching issues from their own perspectives and background. There will be blind spots and a lack of seeing things from the other's viewpoint.
Shouting matches and focusing on 'proving that you are RIGHT and the other person is WRONG' only makes both sides dig their heels in deeper. The aim is not to win or humiliate your partner but to reach a shared understanding in spite of differences of opinion.
Often we expect the other person to be open to changing their position but rarely consider if we are willing to do the same in return.
Talk (calmly) about what evidence you have used to help you reach your viewpoint. Encourage your partner to share the same. Look for common ground and ask probing questions. Try and understand their perspective and ask them to do the same for you. It's not easy and it takes effort, especially when it's an emotive issue for one but not the other.
For example, I've been talking to my partner on and off about all the trans stuff for almost a year. He gets some issues but not others. He can appreciate some aspects but still feels others are maybe hyperbole. I try not to go on and on about it and sometimes things get a bit heated. We haven't fallen out or anything major but he does get frustrated and annoyed at times so I remind myself to reign it in if I'm rabbiting on about it too often.
Slowly though, he is coming round. I've not pressured or forced him or tried to insist he's wrong and I'm right. He might occasionally say things that sound a bit ignorant or sexist or misogynistic but I don't label him as an irredeemable monster. Over time, he has started to listen or watch videos on the topic on his own. The sporting stuff has resonated with him. He is sometimes the one to point out to me 'hey I saw this article in the news' and then we might have a short chat about it. I encourage him to express his views and I try not to be judgemental if he doesn't have the exact or perfect response I was hoping for. When I showed him some of the prison stats some weeks ago that seemed quite a lightbulb moment for him. I think he's slowly starting to understand and appreciate the different strands of the debate. Of course the crucial bit is that even if we don't agree on everything, he is still encouraging and supportive of me going to events.
There has to be mutual respect for each other even if we might have to agree to disagree on some points. Most people simply haven't spent much time thinking about trans ideology or the gender pay gap or whatever. They have more important things going on in their lives and these topics aren't high on their list of priorities. It's different if you take an active interest in it and have been following all the research and reading up on the arguments. Other people simply don't have the time or inclination to do this.