On ships such as the Santa Maria, why was having the rutter at its rear?

Question

specifically talking about why it was an advantage of having it at its rear opposed to having it on the side of the boat.

Answer 1

The Santa Maria was a fairly short, wide ship compared to the ancient Roman and Norse vessels which more commonly are known to have had their rudders mounted at the side.  Although they did have the side-mounted rudder, it was still as far astern (at the rear) of the vessel as practical.  A rudder mounted at the center line of the vessel on the stern, as on the Santa Maria and the vast preponderance of modern vessels, makes for better, more efficient steering in both directions.  It also frees up both port and starboard gunwales for things like docking, where you don't have to worry about smashing the rudder against a piling or dock.  It is also less exposed to being destroyed during a battle.