Anyway, the point is that the folks in the US objected to a geographical name that was no longer appropriate - their independent country was no longer "British". And that seems to me to be appropriate for the Irish living in the Republic. Their country occupies most of the island of Ireland, is independent, and certainly not British. Why should they accept that they live in the "British" Isles, any more than the Americans should have accepted after independence that they lived in "British" North America?
There's no problem calling the archipelago "the islands of Britain and Ireland" or something similar - it's more accurate for a start, and less irritating to patriotic citizens of the Republic.
So - what was the original question?
After 2 pages of debate I think you have hit the nail on the head Iain ...
... however in a way I can see why this causes so much confusion. Ireland being such a small nation it is easy to amalganate us into the UK due to proximity & past history. The amount of people I have met that think this is true used to always amaze me but if they have no real interest in a small nation off the west cost of Europe there is no reason why they should know it as a matter of course ... and this is probably where the nub of problem lies ... the reason people do associate the entirity of the Brittish Isles as they do is because of the title itself being out there and in the main stream so the need is to re-educate and spread a bit of our own propaganda
The word propaganda is not neccessairly a bad word as a lot of people seem to associate
Propaganda is the dissemination of information aimed at influencing the opinions or behaviors of people.