Canada, Australia, the US, perhaps Latin America. Etc.
On the surface it strikes me as superficial but it is popular among those who emphasize a pan-European identity for political purposes. Much of this is complicated and found in issues of psychology and development. Speaking as an American I know Frederick Jackson Turner saw America as something new in expanding west. His frontier thesis alone calls into question the idea that the US is merely an appendage of Western Europe. Plus white Americans do very much distinguish themselves from Europeans in self-conception. Add to that America's Anglo core and it gets even more complicated. The British themselves have a rather iffy relationship with the idea of being European. So do, say, Russians for that matter.
And if I can say this as an American other settler countries likely have other qualms. Is an Argentine just a European outside of Europe? Place, nevermind genetics, does have an impact.