Actually no, it's not arrogant. If referring to your continent, you would be correct. For example, European vs American. This is rarely the case. Usually, we are referring to nationalities. In the case, a Canadian would be a Canadian, not an American, because "American" does not refer to his country. The same applies to other countries in North and South America (no, I didn't forget central america, it's a region of North America). "American" does refer to the country of a citizen of the United states of America.