I feel a bit sorry for the OP as she has been a bit misunderstood.
Unfortunately OP, I think you came across as slating working mothers, and saying kids are better off with mum at home. And although I agree this is great, and fab for some, it's not always great for some kids, and not always the cosy, lovely, mumsy, Walton-esque scenario that you paint.
I know some SAHM's who are complete eejits, who barely pay a scrap of attention to their kids, who are on their phones 24/7, who scream at their kids to STFU when they whine, who dump them on nan at the drop of a hat so they can piss off out with their mates, and who F and blind at them. And some working mums who are fab mums, who think the world of their kids, and who spend every moment away from work with them.
Then I know some SAHM's who are hands-on mums who do loads with the kids and do go to every play, sports day, school play etc, and pick them up from school etc, and whose kids are lovely, happy, secure, lovely kids; and some working mums who have no time or patience for their kids, and work and throw themselves into their career/job because they really can't be arsed with their kids, and who have no connection or relationship with their kids now they're teenagers/young adults.
So there are good and bad in working mums AND SAHM's.
You are correct though OP, that it's bollocks to say that children benefit from both parents working. That is strongly implying that the mum staying at home, means the kids will automatically want to be a SAHP, they will not want to go to uni, and they will not want a career.
Rubbish. I know many, many young adults whose mum was a SAHM, who went to uni, travelled extensively, and who now have a successful career. I know some people who have mums who are now 50-55, and the mums haven't done paid employment since they were 20; yet the (adult) children have still gone onto higher education and a successful career.
So a child whose mum is a SAHM is no more likely to want to be a SAHM herself, than a child whose mum is a 'career woman,' (who sent the kids to nursery and childminders,) will want to have a high flying career themselves, and send THEIR kids to nursery and childminders.
One of my neighbours is a very successful business woman with 13 shops throughout the south, and 33 houses she rents out; she is 55, and has been self employed since 18. Her only child (a daughter age 34,) got married at 20, and now has 3 kids aged 3 to 11. She wants another 2 children before she is 40, and has no intention of stopping her SAHM life. Her husband works and has a successful career, and they are both happy with their roles in life, and in their family.