The abbreviated term "America" is short for the full name "the United States of America".

The Book Cosmographiae Introductio, states,
"I do not see what right any one would have to object to calling this part, after Americus who discovered it and who is a man of intelligence, Amerige, that is, the Land of Americus, or America: since both Europa and Asia got their names from women".

That is how the name is derived.

Because Canadians insist on calling themselves Canadians. but say A .this is to insist that A is American Too. Would you not think Canada owning the greater amount of America would be so polite?