I'm afraid you are missing the point my friend!A European is a person belonging to one of the cultures that are found in the European continent.
We may all have different characteristics and varied ways of thinking, but we all have to common elements that make us part of the same family. Our European culture is based on 1)the greco-roman culture and 2)christianism.
Everything, from our way of seeing life, our democracy, our customs, our institutions, and the fundamental belief of respecting Human rights (against death sentence for ex.), all that is so, because of the existence of a common cultural basis which we share with no others (not even worth it to compare us with Americans!)
You are Irish you say! That is great! But you also belong, just by being Irish, to the broader family of the Europeans!
Be proud of it!