I suspect you're thinking of this answer I wrote (under my former username) about how white children were raised to be enslavers. From the answer:

Caroline Howard Gilman, born and raised in New England, moved to South Carolina in 1819 and in 1832, started a children's newspaper of her own. Originally known as "Rose-bud", she renamed it "Southern Rosebud" (or "Southern Rose Bud") then "Southern Rose." That she was a New England transplant is significant - she grew up around anti-slavery activists but within two decades of living in the South, became a vocal advocate of the Southern lifestyle and culture. In her opinion, [Lydia Maria] Child was filling children's head with tales about equality between men and women and people of different races but Gilman saw it differently; Black people didn't want to be equal - they enjoyed serving white people and she set out to help white children learn that lesson. Gilman worked to walk a very specific line: the plantation system wasn't perfect and slavery did have some downsides but overall, a hierarchy with white men at the top was the way things were supposed to be.

In the stories of the Rose-Bud, Gilman presented a South that she hoped would be embraced and enacted by her young readers as they grew older... The South, as it appeared in Gilman's children's stories, exemplified a particular domestic paternalism that sought to normalize the gender and racial hierarchies of a slave society by tying characters together with bonds of affection instead of bonds of ownership. The children and adults in Gilman's writing model mastery and paternalism for white boys and girls so that they could rule with kindness instead of violence. Gilman tried to soften slavery by showing it as an organic institution deriving from the gentleness of family bonds, but a close reading of her stories reveals that she could not write out the violence underlying southern society.

One thing to clarify given the context of your question - these weren't just about how to treat enslaved people, it was about how to treat all people racially coded as Black. This included free Black adults they might encounter. White children were routinely taught they were entitled to ask for papers or to call a Black man much older than them "boy." White children in homes that did not use the labor of enslaved people may or may not have gotten that same message, depending on how their parents approached the topic. (And to be sure, there were white children raised among enslaved people and taught a specific way to treat them who refused. The Grimké sisters, Sarah Moore and Angelina Emily, are probably the most well-known.