So, why do we associate corned beef and cabbage with Ireland in the first place? Part of it has to do with marketing and advertising - corned beef was a big industry in the United States, and companies like Hormel did a great job of selling it as a "traditional" Irish dish. It's a bit like how we think of tacos as a quintessential Mexican food, when in reality they're a lot more complex than that.
Another reason for the confusion is that corned beef and cabbage does have some roots in Irish cuisine - it's just not as central to the Irish diet as we think. The dish was actually popularized by Irish-American communities in the United States, who adapted traditional Irish recipes to use corned beef instead of bacon. It's a fascinating example of how food can evolve and change over time.
Classic corned beef with cabbage and potatoes for St. Patrick's Day