Ah now, do people get bothered over Southern Ireland?
Becuase this country is just that - a country. It has a name, a Constitution, 3 branches of Government, representation in the United Nations, etc. Why should anyone use a name, to refer to this country, that is not the name of the country ?
Northern Ireland is what it is. A part of the United Kingdom, 6 of the 9 counties of Ulster. Abbreviating it to The North is easy to see and understand.
The same cannot be said of this country; there is no equivalence between our status in the world, and that of Northern Ireland.
Referring to this country as The South is, IMHO, dismissive and an insult. Unionists use it which ties in to their historic attitude to this country. Sinn Fein use is because they aspire to a 32 country Republic and are ambivalent about acknowledging the reality.
Referring to this country as The South means the rest of the island that is not The North. That is wrong. That is the tail of the dog referring to the rest of the dog as 'not Tail'.