Curious ...I know a girl who dad is half Italian and irish and her mom is irish as well....?

I think she's proud of the Italian side of her family more than any other. It also depends on the type of people she lives around. If they're mainly Italians, she will find the need to try and be more Italian. It's not that she lacks confidence, but self pride. I don't know where your friend lives, but if she lives in the kind of place I do, you will always see Italians wearing shirts that say Italia, and showing their pride so much. I wear the shirts and all but I don't over do it. But overall she should be proud of herself and what she is, she can never change that so embrace it.