As with many cultural differences across the Americas, this difference between most of the US and Canada and most of Latin America is not inherently from the Americas but largely derives from differences between British and Iberian culture.

There is a concept called the Hajnal line, after the Hungarian/British economist John Hajnal who first described it in a formal setting, which divides Europe into different regions based on marriage pattern: in most of Northwestern Europe, people would marry later, and adult children would be expected to find their own homes and live relatively independently, a phenomenon known as ‘neolocality’. In Eastern Europe, Ireland (traditionally), and the Mediterranean (including most of Spain, Portugal and the old Kingdom of Naples, there was greater incorporation of the so-called ‘nuclear’ family with the extended family, and people would live with and eventually support their parents for longer. The first correlates slightly with Protestantism and levels of industrial development, while the latter correlates with East Orthodoxy and Catholicism (some might draw comparisons with popular characterisations of ‘Protestant work ethic’ and ‘Catholic family values’, though these are woefully simplistic).

Historically the Western system of neolocality developed in Northwestern Europe in the early modern period, and was expanded gradually with industrialisation and greater social mobility as young men left for the city for a wider variety of jobs, rather than sticking to their ancestral farm. With the advent of women’s rights this later expanded to include more independence upon adulthood for women, too.

Parts of northern Spain actually started to switch to a similar system, during a period of major French cultural influence under the Spanish Bourbons and onwards, but by this stage much of Latin American society had already been laid down. The US and Canada took after Britain, though of course large minority communities see far more involvement of the extended family later in life.

There were many other forces: the Industrial Revolution (which reached the US from Britain before it reached Latin America) led to far more social movement to work in factories and cities, which contributed. And it was only in recent years (1971 in the US, officially) that 18 was taken to be the age of majority (rather than 21), and the expansion of the college population across the 20th century has also led to this particular age being seen as the age to leave home.

Exceptions of course. The US has been diverse for a very long time, and Hispanic-, Asian-, Eastern and traditional Italian- or Irish- or Eastern European-Americans have tended to stick with the more extended family-orientated model for longer, though this tends to weaken as generations roll by. African-Americans of course as a whole have a very different and tragic history of family dynamics due to the treatment of families under slavery, but which is complex, nuanced, subject to some gross simplifications and which I’m not well informed enough about to discuss. But I assume from the post that OP means the majority of the US, whose societal norms were largely driven by Western European and in particular British norms from the last few centuries.

Will add references below in due course.