I would suspect most operators would use CIA as the alternate, so already the captain had probably added enough extra fuel to be able to hold for 20 mins and then extra on top for the longer diversion to Naples. We carry very little extra fuel these days unless we see reason to.
CIA and FCO are so close that weather is likely to be similar at both.
It would be guess work to say why an approach wasn't flown, but we could guess windshear reported / magenta on weather radar, personal preference and gut feeling. Sometimes it pays you also to divert early... reason being, lets say the last two aircraft have gone around, both planning to divert to Naples, suddenly there is the possibility now an unknown arrival delay into Naples as the flights diverting build up. By diverting early, you can save yourself struggling late with fuel on diversion.
I once decided to have a go at an approach into Toulouse with CBs in the area. We went way over the flap limit speed in positive windshear and therefore had to delay the return flight awaiting maintenance work. Sometimes it is best to be prudent and just divert.
I would also add a difficult situation for a captain is this: making an approach in very rough weather, scaring the passengers, go around then diverting. Now you will most likely have some passengers on board who are very shaken up and the last thing they want is flying anywhere else. So you potentially have some passengers who want to get off wherever you are (convinced they narrowly escaped death), some want to stay and continue to destination; a mix of bags in the aircraft hold. It can make the day very very long and stressful. And yes, this does happen!