1. An uninhabited, remote island
2. In the Caribbean
3. Containing trees, coconuts, and various things that wash ashore
4. Inhabited by birds, reptiles, and a few other small game
5. All the fresh seafood in the world
6. Did I mention it's a remote island?
7. In the Caribbean

1. Cockroaches.  They were all over the place.  That would be enough to pretty much change my mind about this whole thing.  But it's such a small island, you could probably just kill them one by one and be done with it in a few days.  Or you could get used to eating a tasty little fried treat.
2. Rustic-ness.  There's literally nothing around for hundreds of miles.  No electricity, running water, plumbing, shelter, or cell phone towers.  Technically, the ocean would cover the whole running water and plumbing aspect of it, but that's about it.  None of these things are really downsides in my mind.
3. Size and vulnerability.  It was an incredibly tiny island, so I wouldn't imagine it would survive a hurricane too well.  Plus, the guy said some of the debris on the shore suggested the island was used by poachers in the past.  Poachers usually carry guns, so you'd be pretty screwed if they decided to come back.
4. I hope you like seafood, because that's all you're gonna eat, except for the occasional lizard or seagull.  And I'd eat a lizard before I ate a seagull.

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