This bullshit gets really tiresome. The reason why the Gaels called themselves Gaels after they "invaded" (though the use of that term hasn't ever been proven--the Gaels have moved between northern Scotland and Ireland for a very long time), is because it was Irish Gaels who did the the majority of moving back and forth between the islands until the time of the Irish plantations. Oddly enough, Irish Gaels spoke Gaelic at home in Ireland as well.

Is it really that hard to figure this out? Why don't some of you pick up a fucking history book.