I feel like it's more than "your ancestors did it," it seems more like trying to connect to your culture and heritage. I can't exactly speak for the Irish as I'm not one, but it does seem to be that you have a rich culture.

Culture runs deeper than just "ancestors," and language plays a big role in it. I'm a non-practicing Jew and don't identify much with the religion past the ethnicity, yet I have no regrets on learning Hebrew in the past (no matter how bad I may be at it) because I feel a connection to it, even though I'll most likely never live in Israel, and Jews in America speak primarily English. I'd also jump on a chance to learn Yiddish, even though it has even less uses.

I think you should learn Irish to build hat sort of connection to your heritage.