Your “genetic make up” has nothing to do with you “feeling as much Libyan and Irish”, that is do do with your upbringing, where you have lived and your cultural experiences.
I agree with you, I still 'feel' Welsh. But obviously I am not.
A typical Welsh surname passed from my father, which he was passed from his father; 'Knowing' my father's family were from Wales and he had been brought up there, learning Welsh customs etc. All those things makes me 'feel' Welsh.
But I'm not.
It's a complex thing, how people feel.
Presumably the DNA is a truth. I think we're still working out what that truth tells us about ourselves.
I never 'felt' English growing up, I was always told about where my ancestors had come from and England was a small, not insignificant part but less than a quarter. But according to my DNA it's the majority.
So I do agree with you Dive