I am looking for a specific expression or phrase that means "a child is the exact opposite of his parent(s)"
Is there an opposite idiom, phrase or expression of the saying:
Like father, like son
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“The pendulum swings.” is a simple sardonic phrase I've heard.
“He's a preacher's son”, (probably an Americanism) which can be used when in fact a preacher has nothing to do with it. The son of a police officer may end up in trouble often and on drugs. Equally sardonic, “He's a preacher's son”, which to certain rural folk says quite a bit.
Just a couple ideas.
Edit: Just thought of another slightly related phrase, depending on your needs:
“The shoemaker's children go barefoot.”
The expression "must be the milkman's son/daughter" accomplishes close to what you want. While a bit dated I think it's still widely understood. If you're unfamiliar, it implies that the offspring is so different in some way than the father, that they must be the product of adultery.
I don't know who he/she takes after.
Lamont stayed behind, looking disgusted. “That boy is just so cranky,” Mr. Otis told Ira. “I don't know who he takes after. Breathing Lessons
[I wonder/don't know] who he/she gets that from.
I don't know who he gets that from as his daddy and I both love to eat. The Abundant Life Project
"Changeling" means a child that was switched at birth in various mythologies, "Cuckoo in the nest" means being different than your peers, but it also kind of means not the actual child of the parents, which is different that just being not like the parents. "Like Chalk and Cheese" give the idea that two people are very different, but not specifically parent and child.