Do you consider yourself to be part of another nationality? For example, if your Mum is from France, do you consider yourself to be part French? I've never really understood it to be honest. Two of my grandparents were Irish but I don't consider that makes me remotely Irish. I was born in England, raised in England (apart from a stint in Wales) so I'm English.
my great grandparents were Irish being descended from norman invaders from belgium, one of my grandparents was welsh. I think I am English through birthplace and culture(debatable) but I see myself as European. The Irish connection I find appealing but have no wish to be any particular nationality.
I'm English, I suspect there is some Welsh on my mothers side, but I consider myself completely English - and not European. To me Europe is across the water.
I was born in Scotland to a Scottish Mum and an English Dad - though I have spent most of my life in England, I still think of Scotland as home and Scottish my nationality.
My maternal grandfather was Irish (from the South) before partition. That makes me 25% Irish, which apparently entitles me to an Irish passport. Haven't yet taken up the offer, but might do if they are cheaper than British ones.
Like many Australians I am a mix. My ancestors are English, Scot, Danish and Polish.
However I don't think of myself as having a cultural heritage from any of them. I prefer to make my own culture rather than be a slave to someone else's ancient habits.