Our proto-sociologist is waxing a bit too poetic about "children." But by 1500, northwest Europe (England, the Low Countries, some of France and Germany) did have a different culture/economy surrounding adolescence and young adulthood.

The most visible and famous (okay, "famous") manifestation of this is what scholars call the European Marriage Pattern. Although John Hajnal originally developed the idea for a later period, subsequent scholarship has shown its origins in the late Middle Ages. The basic thesis is that people in so-called northwest Europe waited longer to get married than people elsewhere. More specifically, that women waited longer. In practice, the stereotypical practice of that is teenagers moving from rural areas to a nearby city to work for a few years to earn a bigger dowry (women) or put themselves in a better financial place (men). Generally in this framework, we're looking at peasants and middle-class adolescents. Teenage girls and young women most likely found work as domestic servants. Teenage boys and young men might work as servants; the lucky would would indeed get an apprenticeship in a craft.

The inducement for immigrating to cities wasn't necessarily desperate poverty, although that was sometimes the case. But really, we're just talking about kids, and probably their families, who saw better opportunities in the city than in the countryside. One apprentice/servant (it's not quite clear) actually loaned out some of his possessions to his employer's patrons on the promise that the employer would repay him...since the source is a lawsuit, you can guess how that turned out. Or, one servant named Isabel (no surname given) showed up to her new employer's house with a substantial set of possession, including multiple sets of sheets, her own mattress and quilt, and other cloth/clothing goods. (Since the source of this is also a lawsuit, you can guess that her employer did not wish for her to keep these afterwards.)

There is indeed a contrast here between English and Italian cities. Italian statistics on marriage age are a little off because families (across the social scale) sometimes lied about their unmarried daughters' ages to make them more attractive potential partners. But for England, we're looking at people getting married in their early/mid twenties, or maybe very late teens. In Italy, girls married earlier in their teens, and men married later, particularly upper-class men.

The EMP is a really big deal, and there's a good amount of scholarship pointing to it as a driver of superior economic growth in England and the Low Countries versus southern Europe. But it's not the only way that we would see parents outsourcing adolescence.

First, there were cases where children--possibly as young as seven--did indeed leave home to go work. I've not read tons about this, but it's mostly in the vein of "no, seven-year-old boys who started working for a master craftsmen weren't apprentices; far more likely, they were servants and stayed that way."

But also, by the 15th century, it was common practice for upper-class teenage girls to spend a long period away from their families. The major goals here were for young women to gain more skills managing an aristocratic household, learn systems of manners and other rituals more formally (from an outsider's perspective/eager to observe everything to fit in, basically), and expand their social networks for potential marriage and economic/political connections for their natal and marital families. Barbara Harris argues that in some cases, girls did end up as glorified servants. But in others, they were essentially surrogate daughters.

One major difference between the elite system and city workers: in the former, parents had the major say over potential marriage partners for their daughters, although Harris stresses how much of her evidence shows parents taking their daughters' wishes into consideration when negotiating. But when apprentices and domestic servants in city crafts and households were thinking about marriage, their employers often tried to have a say. Barbara Hanawalt even dug up some lawsuits surrounding, shall we say, disagreements between apprentices and masters over who they could court and marry.

So what you see in these cases isn't so much about different English and Italian theories of childhood--it's about ideals of marriage preparation.

For example: in English and other northwestern cities, as above, it was much more common for girls (especially) to work to earn a bigger dowry. This wasn't the practice in e.g. Italian and Spanish cities, but that doesn't mean that families dumped their daughters onto a marriage market and turned away. Some southern cities had charity supplements--from a civic pool--for dowries for young women/their families who didn't have enough on their own. Not that there was enough to go around--the idea of the "deserving poor" has far too deep roots--but still.

So the original statement is rather an exaggeration, but there's still a solid observation at the heart of it.

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You might also be interested in my book How to Slay a Dragon: A Fantasy Hero's Guide to the Real Middle Ages, which uses fantasy tropes to talk about the cool parts of the Middle Ages. Including, yes, the European Marriage Pattern--how else are you going to learn How To Flirt With The Barmaid?