This is an excellent question. I have no doubt that some of these stories of islands disappearing are over exaggerated by many people pushing for climate reform. Or simply the islands are being eroded away. However, there was a story I read in school that I found quite interesting. I'll link it if I can find it. It basically spoke of a very small patch of land that a group of islanders would frequent in order to fish. Well, this patch of land is now completely covered in water. Not eroded away, just completely engulfed. It even has satellite photos from a few years ago, taken at the same date in time showing the changes.
EDIT: I am unable to find the article. So I guess this point is moot since I can't back it up. This is a good read however, even though it's CNN
You're making this island disappear
There used to be an entire civilization that existed on the western coast of India, back when there weren't nearly as many humans. But the island chain is under water now, and the civilization gone. Surely no one argues that was man-made. The climate changes. In fact, it has never been static.
Do you ever step back and ask yourself why this has become an emergency in the last 40 years? And do you ever ask yourself how, in spite of the flawless math and hyper accurate instrumentation they keep screwing up the predictions?