It happens that I am a man who cooks, cleans, and cares for the children in essentially the same way the stereotypical 1950s housewife did, while my wife works. By good luck and good planning, we're able to make this work out. It is not necessary for both of us to work outside the home.
An alternate take from Mr. Blagojevic's is that capitalism run rampant has forced the working class into a situation in which both partners in the family must work to make ends meet, leading to the aforementioned rise is disposables. I find the whole thing somewhat tenuous at best, but if you insist on "less cooking and housekeeping" is the cause of plastic in the ocean, then the cause of the cause can be attributed somewhat better to insufficiently fettered capitalism than it can be some vague leftist agenda.
That wages of the working class have been essentially flat for decades is undisputed. That Capitalists are doing increasingly better is undisputed. That the wage gap has been expanding for decades and continues to do so is undisputed. It is, from these undisputed facts, a very very small step to "insufficiently fettered Capitalism is the major cause the both-parents-work situation"
Of course the leftist agenda did include the idea of choices in work, but as usual the Capitalists co-opted this and turned it in to "No, no, it's not that we would prefer that We Get the Money and You Do Not, it's OPPORTUNITY!" but that is an obvious sham.