in some areas, children do NOT need tuition from someone who has made academic study of that area, or even from someone with expertise in that area (eg computer games, and of course this is a well duh point to make). they will reach excellence on their own.
in other areas, and the one which came to my mind was skateboarding, children seek out for themselves the expertise to help them get as good at the activity as they want to. they will happily spend 3 hours a day for years and years trying and failing to do that thing where you jump up and spin the board under your feet, land on it and keep going. They hang out with older skateboarders watching what they do, they take tips from the more expert ones when offered. And they don't need parents to find them a skateboarding tutor or school teachers to timetable a NC skateboarding hour every day in order to make sure they devote enough time to it. They themselves seek the help and tuition they need from older experts.
Self motivation is the key not only to learning but also to finding the advice and expertise and, yes, teaching you might need in order to learn as much about an area as you want to. A big advantage of schools is that they gather the advice, expertise and teaching provision in a fairly wide range of areas of human knowledge under the one roof. A big disadvantage of schools is that children have to access the advice, expertise and teaching provision on other people's terms as far as timetables and curriculum and so on are concerned. Schools just can't, by their nature, be as good at just-in-time personalised self-motivated learning for a child as the freedom to chase their current interests with support and advice from parents and the contacts of their friends and relations would be. And all those museum/zoo/national trust type staff just waiting for a persistent child to come along with questions. The world is full of trainspotters who love nothing better than to talk about their passion.
I can see that some think that it's important for children to be prepared to learn what other people think is important, and not to be expecting people to be prepared to help with their current passion at the drop of a hat. But the law says I should be providing an efficient education for my children, and I can't think of anything more efficient than educating them by helping them learn what they want to learn when they want it. Good schools do a splendid job of persuading children to learn what's on the agenda for today but I'm after maximum educational efficiency
so a reason to send a child to school would be about accessing, under one roof, all sorts of expertise and experience at communicating ideas to children.
And a reason not to be would be about maximising the efficiency with which a child accesses the knowledge and understanding and expertise they are interested in at any particular time.
There are good reasons why a lot of HE children go to FE colleges for GCSEs and A levels and diplomas - they consider it a way of getting the best of both worlds.