First of all, there is the interest of the Crown of Castile to reach Asia through a different route than the Portuguese. After the fall of Constantinopolis to the Ottoman Empire, the European trade of spices was extremely affected. Whereas the Italian territories fought for agreements or directly fought the Ottomans, the truth is that there was a huge demand for Asian species and silk which could not be fulfilled. The Portuguese started their explorations in the early 15th Century sailing south, circling Africa, until they reached India. The other possible route was just sailing west. Who were the main competitors of the Portuguese in this? Castile. There had been attempts to do this, as you may already know that the Canary Islands are now Spanish territory and their language is Castilian but the only reasonable way left to go was sailing West.
Secondly, despite the marital union of the Catholic Monarchs, the enterprise was fully Castilian, as the Crown of Aragon did not have funds for this. What was the last territory that Castile got from the Moors? Granada. It was natural to continue certain expansion to user that army. This led into certain conquers in the North of Africa but finding a route via Africa would have meant trouble with Portugal (this was later settled by the Treaty of Tordesillas).
Third: There are theories that say that Columbus was, actually, not Genoese. Now you can think whatever you want, and always take theories with a pinch of salt, but it could have been perfectly reasonable that Columbus, who signed Colom his documents would have been a subject of the Crown of Aragon - since Colom is how his name is written in Catalan and Catalan was the most spoken language in those territories. Some people say that he could have been Jewish (at a time where Jewish were to be expelled from the Iberian Peninsula) of Catalan or Majorcan origin, or even Catalan/Majorcan himself. Before you think theyโre crazy, just take this theory with a pinch of salt and itโs not that crazy if you take into account that he did not have too much trouble in reaching the Queen of Castile since he could speak the language. Even if he were Italian, quite a chunk of Modern Italy belonged to the Crown of Aragon and as other answers point, he could have just changed his origins to pretend he was better.
Nevertheless, I think that the final reason is that it seems a bit more logical to depart from an Atlantic seaport than a Mediterranean one.
However, there is not much clear. What we surely know about Columbus is that he hid whatever he could about his origins.
