I don't know if the reasons/motivations are always quite as unpleasant as they might seem, e.g. arrogant, entitled, thinking they and by extension their kid should and must be the best, etc.
I think some of them might just be acting the same way lots other parents do, by assuming their children are going to be like them. Some of them are probably just going with what they know, which is a school trajectory of high academic achievement. It's still not a great approach, obviously — children will be who they'll be, not mini-mes — but you see it happening much more broadly than this, with parents who, maybe, place a lot of importance on appearance imposing that on the kid, or sporty parents assuming their kids will be great at sports and pushing that on their children, and all kinds of stuff really.
If two high academic achievers meet and have kids, their combined experience of school is that you fly through it at the top of the top sets, are recognised constantly for your academic achievements, find the work and the homework reasonably easy and are rewarded with top grades for putting in effort. That's what they're familiar with and know how to deal with. They don't know what it's like to be academically average or struggling, and have no idea how that situation plays out or should be handled. Their own experience is of being told that average grades aren't good enough, and that they need to work hard for top grades. Why wouldn't their default assumption be that their kid will be much like them in this respect, and if the child's not getting exceptional results that means something's not right with the school? (I mean, it shouldn't be their default assumption, but humans aren't always perfectly rational.)
I'm sure some of the parents you're talking about are just arseholes, but I wonder whether some of them are parents who only know how to use a hammer, when their kid is a screw.