@Newbutoldfather - I'm not trying myself in knots at all! To me, the maths is pretty obvious. But people often struggle to understand the implications if you keep it too abstract, so I thought a concrete example could help.
And yes, I absolutely think that I know better than the IFS about the likely behaviour of people in my own situation.
I generally don't trust that politicians etc know better than me unless they back up what they're saying with a credible, fact-based justification: because I'm pretty good at understanding complex concepts so it's basically never the case that I "just don't understand it".
But in this case, it's more than that. It's that I have knowledge they don't.
I see so many families at my level of income making exactly this decision: private + both parents work full time versus state (grammar or nice comp) + mum working part time and running kids round to lots of activities.
And where finances are good enough for private to be an option, it's the Mums who make the decision. Because it's them who will be more affected: even in equal families, it's almost always the Mum who plans and schedules the activities and juggles the logistics; mainly the Mum who has to re-schedule meetings to manage the times it doesn't work out (or else asks the Dad to if she can't - but it's still the Mum making sure it happens).
I'm one of the Mums who has switched to full time to afford private. And I know I couldn't juggle full time with state. Not without DD missing out hugely, which isn't a choice I'm going to make. I depend on the school having most activities on-site, great wrap-around, and lots of flexibility.
I've seen friends decide that the proposed VAT hike makes private too risky, and so go all-out for tutoring for grammar instead. And yes, it's the Mums who made that call and organised the tutoring.
And I can bet that neither the senior Labour party policy-makers nor the IFS include many working Mums in their number... and if they do they probably don't listen to them.