The facts around rising sea levels are widely misunderstood or misinterpreted. This has added heat to a New Zealand news story that went global: "NZ casts off first Pacific island climate change refugee".
Global warming would lead to thermal expansion of the oceans. Sea level globally has been rising at about 1.7mm a year since the Little Ice Age ended in the 19th century, but has slowed down since the high rate of rise that occurred following the last major ice age 18,000 years ago.
To the surprise of many scientists, sea level rise is barely perceptible in the Pacific. This is possibly because, at least in part, there has been no global warming over the past 17 years.
Atolls are formed as sea level rises around volcanic islands. The atolls grow as they are replenished by coral that breaks off surrounding reefs and is thrown ashore by storms. In that way atolls are self-maintaining. They have survived several periods of rapid sea level rise in the geologic past. All remains well, provided humans don't intervene.
The digging up of an island's coral for use in construction work and the building of flush toilets that discharge the effluent into the sea where it affects coral alter nature's balance.