Why do Italians eat fish on Christmas Eve?

12 kinds of fish/seafood for Christmas Eve dinner. The reason being, one seafood for each of Christ's Apostles as they were considered 'Fishers of Men.'

There is also a tradition of eating seven type of fish, 7 being the number associated with God (6 with the devil).

The reason behind the use of fish, on the other hand, is simple: Christmas Eve is a vigilia di magro, in other words, a day of abstinence in which the Catholic Church prohibits the consumption of meat.

...a fish-based Christmas Eve dinner is not part of the Tuscan tradition - It's more of a southern thing, celebrated from Rome on down.
http://italianfood.about.com/od/menues/a/aa121698.htm

La vigilia is as far as I know a uniquely Southern Italian affair, a feast involving seven fish dishes. There's no specific menu to follow; each family has its own traditional dishes it brings to the table. In my family, there was always baccalà, sometimes two different preparations, a big bowl of shrimp and heaping portions of spaghetti all'aglio e olio, a small portion of which was made with alici, or anchovies.

http://hedonia.seantimberlake.com/hedonia/2006/12/feast_of_the_se.html

The Feast of the Seven Fishes is a traditional Southern Italian and Sicilian event. Christmas Eve, known as vigilia di magro, is a Catholic day of fasting; no meat is eaten. Toward evening a family will traditionally break the fast with a feast of seven fishes prior to midnight mass. In America today, Italian-American families continue to follow the tradition of the feast, with some families adding nine, eleven or even thirteen fishes. The seven is believed to represent the seven sacraments.

https://en.wikipedia.org/wiki/Feast_of_the_Seven_Fishes