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Indeed it is a jerk response.

They were bragging that primary school is mostly busy work while ironically making a primary school mistake.

I'm with you. It's like the most ironic setup possible for an error in grammar. I was glad to see your response.

Ironically, the error was in spelling, not grammar.

If you’re going to be pedantic be correct. That was a spelling error, not one of grammar.

Eh,the word wasn't misspelled, it was the wrong word.

How is it ironic? I'm assuming that they themselves were brought up in public school and this mistake just makes their point stronger.

If OP's homeschooled kids were the ones denigrating public school while making spelling/grammatical errors then it'd be ironic.

OP showed he isn't qualified to judge.