Estadunidense

So i found the other week that the proper way to describe myself is not as Americano but as Estadounidense. Since I found this out I´ve talked to some people and all of them insists that Americano refers to the continent and that they are just as Americano as I am. I thought I could win by pointing out that they would never in any situation refer to themselves as Americano and understand me perfectly when I use the term but I couldn´t win any coverts to my argument