I think some people don't realize why it's an issue they want to pay for a son/grandson not a daughter/granddaughter, SQ. If they thought it was horribly, intrinsically unfair, I'm sure they wouldn't do it.
When I've seen people express that view, it's usually because 'it's the family school' or 'I loved it there' or 'DH loved it there'. The implication is that the advantage is limited to the time at school - and it's merely an unfortunate coincidence that there's no such pleasant family tradition for the DD.
I suppose what I'm thinking of is my dad's generation, lots of whom I've discussed this stuff with, or with their children. My dad has no idea that his private schooling conferred extensive advantages that far exceeded his time at the school. He passed the 11+ and will always say he had a normal state education (which for his day it was - his time at what is now a private school was funded by the state). That school, however, being a long-established boys' school, had closed scholarships to Oxbridge, so he also got 6 years at university on a closed scholarship. That means that the university had to give a place to someone from his school - or not fill the place at all. And look at how many people from Oxbridge even now end up in politics/high powered jobs.
Because my dad doesn't realize that his education conferred any special privileges that were gender-specific (though patently it did), he has no problem with the idea of sending a boy to private school, even if that school is better funded than a girls' school, gets higher results, is more expensive, and has more scholarships on offer to its pupils. He just assumes that this is the sort of school where he 'thrived'. But he thrived in large part because the school conferred large advantages on its (male) pupils. OTOH, many women of the same generation did not find their private school stood them in especially good stead. Certainly today, although girls' schools send many pupils to good universities, they also by and large prepare those girls to struggle at university, because the qualities universities reward are not IMO those girls' schools often teach. I am dead biased here, I know, so this last portion is just my view! 
I think there is something in it though - that people don't examine why they found private school so good or important for boys but less so for girls.