Question

why is not the president in Asia continant but why is the US continental president?

Answer 1

It should be noted that North as well as South America are contients but, not countries. Therefore, not only do they not have the same political leaders, but they also have various countries and corresponding governments.
For example:-
Canada and the United States are two different countries in the North America. While Argentina, Brazil and Venezuela are just a handful of countries located in South America.
Therefore, the United States calls itself "America" and its citizens 'Americans'.