Lechon/ cerdo/ marrano/ puerco/ pernil
There are, of course, two reasons why Hispanic people eat swine of various descriptions for special occasions. The first reason is religion. In the 1400's Spain decided to convert or expel the Muslims and the Jews. The deal was that if they converted, they got to keep all their stuff and got to stay in Spain. They were also expected to stop using Muslim and Jewish names. Super Chritians names, like Santamaria, Trinidad, and de Jesus were quite popular among the conversos. But there were many who continued to keep ancient traditions. Chimneys were watched for smoke after nightfall on Fridays, and people who did not eat pork were likely to hear from the Inquisition.
Spain annexed the Canarios in the late 1300's, and Canarios were also suspected of being insincere Christians. many were deported to Hispaniola (especially MonteCristi), mostly for being rebellious. The public eating of pigs was seen as a sign one was a good Christian and not a marrano (as Jewish renegados were called).
The other reason is that roast pork, ham, and pork sausage are all delicious. The Sandwich Cubano is made of both roast pork and ham, along with cheese, pickles, mayo and occasionally shoestring potatoes.
In Venezuela, capybaras (Hyrdrochoerus hyrdrochaeris) also called cig?ere and carpincho are a favorite for Semana Santa, since early settlers got the Vatican to declare this large rodent to be a fish, and therefore exempt from the ban on eating meat during Lent. Venezuela is running out of these, and they are importing the meat from Bolivia.
Turkeys are traditional in the US because it was closest to the British traditional holiday meal, which was goose. Turkeys were wild could be hunted, while you had to raise a goose or buy it. People were unlikely to give a free goose away. At least not the edible sort of goose.