When I was a boy, elementary school teachers would shudder with disapproval if you used the word kids. "Kids are baby goats," they would say. You would have to start your sentence again and use the word children instead. This seems ridiculous and artificial to us now. It seemed so to the children even then. Kids did not seem to be slang. It was at worst less formal. Predictably, as the teachers aged out of the system and hordes of new kids kept coming along, the language changed. Only in very formal writing, such as a research paper, would anyone insist on the use of children at this point.
We think to ourselves that the teachers were wrong, but this is not necessarily so. The language changed away from what they thought correct and in our self-centeredness we think "See? It wasn't important. Just like I thought back then." Yet when it came into general use in 16th-18th C's it was indeed considered low slang and no instructor would have tolerated it in class or in writing. Over the course of the 19th C it became more acceptable in speech, but still would not have been used in a newspaper or magazine, let alone a textbook. Teachers of the time believed the point was to teach every child a more formal English that made them sound educated and intelligent. The theory is sound. It is good to be able to speak the most formal dialect of your language with ease. The specific rules they got caught up on were a mixed collection of excellent disciplines that enhanced clarity and pure bunkum that had been artificially imposed on English a century or two earlier by pompous pettifoggers, but the idea was sound.
Somewhere there was a crossover area between the days when kids was low slang requiring correction and century later when it was obviously ridiculous. There is even Oxford English Dictionary Facts For Kids now.
There was a nuanced version which they could have advanced, explaining "That word might be entirely acceptable while speaking with your friends, but when speaking with adults, and especially in the classroom, one should use children." Grammar school teachers didn't think that way then, and likely they should not have tried. Not one child in ten would have understood and fewer still would changed speech because of it. Still, they liked to make us be very precise then according to their fashion, so I will hold them to a similar standard now. The Kids Are Alright.