I find this totally unreasonable, why you are really saying is you are pissed off you can't stay at home and also send your kids to private school.
My daughter was privately educated from the age of 4. Shes never set foot in a state school. She's now at university, I worked to pay for that, why? Because it was important to me to give her all the choices, and yes, sometimes in her younger years before salary increases it was hard. Yes often finding childcare during holidays and juggling was a nightmare, Could she have achieved the same at state school? Possibly yes, but the less one to one tuition and larger class sizes would very likely have made a difference and possibly made it harder.
At no point though did I think it was all on my husband, I had to make a decision. And this was mine. Would it have been better had I been a stay at home mum? Honestly, in my situation, no, it would have had less benefit in the long term, I was there plenty, trust me, she may have had day child care, but she never once had a baby sitter, it's about quality.
We simply have to decide what we want and call it accordingly and there is no right or wrong, but it is wrong to chose not to work to privately educate your kids and be then jealous when others chose the opposite.