Your confusion on this makes sense, because there is no universal agreement on the number of continents.

You'll learn a number in school, but not all schools are going by the same system. There can be as many as seven, and as few as four continents. The main disagreements come down to the Americas, and Europe, Asia (and even Africa). There's no wrong way to divide them though. If you view a continent as one continual landmass, then: America, Eurasia, or Afro-Eurasia are all totally acceptable.

https://en.wikipedia.org/wiki/Continent#Number

How else can they be viewed, and why? Well, a large part of viewing them as distinct and separate comes down to cultural views. With Eurasia there has been a strong divide between East and West since antiquity. While Greeks, and Romans, both made conquests into the East, these territories have always been harder to hold because of the large extent of land and the amount of powers that traditionally have existed, which also means it's been harder to extend cultural imperialism into the region, which makes them different. They would then view them as "the other" and othering cultures is incredibly common. Whether it's Persia, or later the Ottomans, there's a strong "us" vs "them" in history.

Historians and sociologists have long looked at this phenomenon, and works like Edward Said's Orientalism https://en.wikipedia.org/wiki/Orientalism_(book) brought the problematic nature of these views to the forefront of academia in the 70s, which has resulted in some change in academia at least, but there are still cultural hangarounds.

Funnily enough, it's the opposite in regards to the Americas which was seen as one continent for quite some time, and the US would lay claim over the influence (to put it very kindly) of the entire hemisphere with the Monroe Doctrine. But, by the middle to end of the 20th century you see a shift where there is a desire to disconnect from (what we would call) South America, and a desire to other them. And while Canadians might not like being called American because of the term's association with the USA, people in the southern countries can get annoyed with the term's more popular meaning in English because they see themselves as American because everyone on the/both continent/s are by their nature American.

In short: there's no wrong way to view the number of continents, the separations other than just connected landmass are mainly due to geopolitics, historical isolation, culture, and othering.