Feminists have been pushing for Paternity leave (and for society to stop shitting on men for taking care of their kids and the household) for years. http://jezebel.com/paternity-leave-why-dads-going-home-with-baby-is-aweso-1489938655
Here's a Jezebel article from last year, one of the first results on a Google Search. Though, really, what we want is joint Parental Leave that both the mother and father can spend, together or individually at any given point between the two of them. (Or mother and mother, father and father, father and nonbinary parent, mother and nonbinary parent, you get the idea)
Making Engineering Sexy: Just reinforces stereotypes of what a woman is supposed to be (Sexy). Far better is trying to target young girls with science education to get them interested in engineering and other STEM occupations while simultaneously trying to alleviate the stigma against women in STEM fields. Both things that feminists are doing.
Build More/Better Nurseries: Are you serious on this one? I really can't tell. Most women who are unable to find support for their children so they can go to work don't have the issue of a lack of nurseries around: It's a lack of money. Besides, Parental Leave (number 1 on the list) would help solve the issue.
Give Free Comp Sci/Jobs to Stay at Home Moms: Feminism is an ideological movement, not a corporation. We don't have data entry jobs to hire stay at home Moms for because that's not how this sort of movement works. Though feminism does try to sponsor STEM programs for women whenever possible (mostly aimed at children rather than stay at home Moms because you need a lifetime of learning about the subject matter to get the job, y'know?)
Teach people to raise their girls tougher and boys prettier: W... what? This... I don't understand what you mean here. Do you mean parents should put makeup on their sons and tell their daughters to "Walk it off"? 'Cause that's the kind of thing that pisses people off about feminist straw-men and has for decades. While we're trying to break down the socially enforced gender roles that lead to "Tough Boy, Pretty Girl, Nonbinary Nonexistence!" and have been FOR DECADES it's not as simple as just reversing the stereotypes or trying to put in a half and half solution.
As for Rape Culture... yeah. It start fights and solves nothing. It's not a solution. It's an expression to encapsulate a series of propositions that explain the sociological implications of a society which trivializes and condones rape in a wide variety of situations while simultaneously demonizing a specific type of extremely violent rape to push the horror of the crime (regardless of it's circumstance) off.
This is why the Steubenville Rapists, who brutally raped a drunken girl and dumped her unconscious and battered body naked in a snowbank near her house, are known as "Good Boys whose future shouldn't be ruined"
And it's also why inmates who get stuck in a cell with a big dude named Bubba getting violently raped are the butt of jokes (no pun intended). Because violent rape is FUNNY if you socially condemn someone!
But because it's such a new term people don't fully understand and people don't like the implications it puts on the society they live in (and often support to a jingoistic extent) it starts arguments. But it's only through education that people will come to understand what it is actually about.