I'm from a college town in California that is very popular for Irish students on J1 in the summers. I've heard that drunken conversation a 100 times:

Dude: you're Irish, bro? That's rad, me too!

Lad: you're wot?

D: I'm fuckin Irish, dude.

L: laughs in Gaelic, no you're fookin naht.

It made me do a look in the mirror, because I too, "am Irish", or at least as much as one can be after generations of banging Swedes and Germans in the Midwest. If it lends anything to my legitimacy, we certainly had an Irish Blessing mounted by the front door, which I read once when I was finally tall enough to notice it.

I started following this sub during Brexit, not out of some fetish or anything and I don't want to speak out of turn or annoy anyone here. Not to be disrespectful or insensitive towards actual Irish people, but it does confuse me a little, how the Irish seem to resent the American usage of "Irish". I can certainly appreciate that you do, but not being Irish, I don't fully understand the Why of it.

In the most boiled down, over simplified sense, is it because it's basically "cultural appropriation"? Is it because every movie set in Boston or Chicago is full of annoying caricatures of mobsters who claim to be either Irish or Italian and yet are never actually either?

tldr: Being Californian, it's obnoxious when someone moves here from Iowa to make it as an actor and starts referring to themselves as a "local" because they've worked in a coffee shop for six months. But, genuinely and sincerely, why is it annoying when Americans claim to be "Irish"?