I suppose it's got something to do with shared culture - after all, Britain and Ireland are virtually indistinguishable; if you were teleported into one at random you'd only be able to tell which it was from the accents and the money (all right, and the newspapers, the motorway signs, just asking people, etc, don't try to be clever). Ireland as a place is clearly far, far more like Britain than any other countries with ties to Britain such as the US or Australia (if you were teleported into any part of America you'd never think for a moment that you were in Britain!). To that extent, they are much of a muchness and I suppose one could say that Irishness is a subset of Britishness in that respect. But it would be a weird way to put it. Surely better to say that they are two countries that are very closely linked culturally.