The knight need somebody to do his work. This isn't anything special. A lot of romanticism played a role in how we imagine it today. And as I said... it was only for low nobility. This was low nobility squires.
High nobility squires were different. Actually there education was more around noble customs... How do you interact with the people at court? It had less to do with helping a knight. It used the same term but was mostly something very different. Romanticism mixed both types a lot. At least this is what I read in the Lexikon des Mittelalters about this topic.
I'm actually currently studying Chivalry for my final year at university.
Basically, knighthood as we understand it was something invented in romantic literature and by poets/story tellers later on. Knights were essentially those that were able to afford a horse, plate mail (or chainmail in the earlier period of chivalry), and had the time and training to use lances, swords, shields etc whilst mounted. Originally, "knighthood" was relatively open - even relatively poor individuals could be knights, and end up climbing the social ladder - William Marshal is literally the single best example of this, especially in English history. He went from a fourth son of minor landholder to the first Earl of Pembroke and Regent of England. Obviously, "knighthood" changed over time - one of the few constants was that it involved being mounted.
Squires and pages were more of an invention - whilst it is true that sons and daughters both were sent out to other nobles households and learnt by doing, they did not fulfill the role that you'd see in say George R.R. Martins Tales of Dunk and Egg - a knight had servants, not young nobility, for truly menial chores. Younger nobility did do chores, but lifelong "squires" weren't really a thing. Definitely not amongst the kind of nobility playable in CK2.