'It must be about how you present your cleverness to the outside world.'
How exactly does a 10/11 yo present their cleverness?
I was streets ahead of most of my peers at that age (having moved, age 7, to a relatively deprived area compared to where we'd lived previously).
I didn't have the guile or the wherewithall to 'present' my cleverness in any way - I just quite liked learning, occasionally answered teachers' questions and came first or second in the rare tests we were given. I had no idea I was clever, until the jeers of 'brainbox' started to fall on my ears in the playground (and, believe me, I'm no Einstein - it didn't take much brainpower at all to get these neanderthals' dander up).
Same in secondary school; I was shy and socially awkward, although I did eventually get a few friends. All you had to do in that school to be despised was do the set homework, and again maybe answer the odd question in class. God forbid you ever asked a question, or joined in a teacher's attempt to instigate a discussion.
Neither was I a teacher's pet - not pretty or sporty and shy to boot - ironically, the only time I remember prizes being given out, my prettier, more popular friends got the prizes for achievement, when my exam scores averaged out at top for the year.
I envy you that you've never come across such a situation yourself, Yellowstone, but I assure you those attitudes do exist, and it is naive at best to suggest a bullied child may be at fault for their 'presentation.'
Op, my two older DCs are at grammar schools, and their school lives thankfully seem to be light years away from mine. DS2 will be going in September, and I'm convinced he'll thrive once there.