Considering the North American continent has several other countries, (even including places like Greenland!) and there is another American continent, it seems odd that the US is the only one that is considered "Mericuh!"
Is it because we included the word in our official title (US of A,) or is there another reason?
This is a feature of English language speakers and is not true of other American languages, notably Spanish where Americans are typically called estadunidense. The Spanish term americano often refers to people from the Americas, a usage reflective of cultural differences between Latin and Anglo- American countries.
Part of the problem is the phrase itself. People from Canada are referred to as Canadians while people from Morocco are referred to as Moroccan. There's no similar way to modify "United States of America" to refer to people from the US. Try saying "US-Instead, English speakers drop the first part of the name and use "American" instead.
a few more responses that may be of interest:
of possible tangential interest