I guess you can make that same argument about USA and America. Canada is clearly America but a Canadian would not refer to himself as American whereas a US national would. Europeans hardly refer to themselves as such but when European countries are lumped together, it has become common to ignore geography and refer to those affiliated with EU membership or bilateral EU affiliation (Norway, Switzerland, Iceland) as European.

Europe is a geographical region, the only question is where does it border neighboring regions (Asia). There is no ambiguity about whether Switzerland or Norway and so on are in Europe. They are.