My 12 year old deserves credit for this question.
He asked "Why do we say 'by accident' but not 'by purpose' "
I was stumped - this is an embarrassing situation! Searching left me cold. The nearest result I could find was Is it correct to say "on accident" instead of "by accident"? but this is a different question.
We also say "by chance" rather than "on chance".
So, can anyone help me be Dad-who-knows-all again?