I'm not sure about the root of the thought, but for some reason people believe than everyone from Mexico to the south share the same language, same food and have the same tired stereotyped vision of a homogeneous “Hispanic” culture.
In reality, Latin America is a huge sub-continent, so the idea of a single dominant culture is ridiculous. Never the less, the image of “latinos” drinking tequila, wearing fruit baskets over their heads and being inhumanly good at every tropical dance is strangely strong in the collective imagination of people everywhere.
 
Again, it doesn’t really make sense, how could you expect the same cultural background in a Caribbean island and in a cold southern South America region where they have never seen a single palm tree? You can’t expect all of them to behave and eat like some local version of Mexico or guayabera wearing Latin lover. 
 
Even though we all have common characteristics, inherited from spain or portugal, our use of the romance languages passed to us are particular to each region. Every country has a different slang, in occasion uncompressible to any foreigner, including the one’s from neighboring countries. Also, both the latitude and cultural roots have a huge influence over nor only the language, but also the nation’s cosmo vision, how they see themselves in the world, their artistic manifestations; typical dances, traditional food and art, etc.
 
Latin america should be studied as a whole but without missing or leaving unseen every nation that forms it, not only as countries, but also every little culture that happens to exist inside the limits of each country. There’s an amazing cultural richness ready to be discovered not only by north American or European tourist, but also by ourselves, the latinos and latinas (given the fact that at  some point we lost the right to call ourselves americans) who are so ignorant about the cultures that surround us. We don’t even need to go outside our countries, thanks to the migration