Link is one of the most well-known characters in all of video games. He is also one of the few characters who is left-handed in most of his titles, except for The Legend Of Zelda: Twilight Princess for the Wii.
The main reason for the change was that a majority of people who used motion controls, the main selling point of the Wii, were right-handed. This change angered many fans who connected to Link in a special way because he was a lefty. Even his creator, Shigeru Miyamoto, designed Link to be a lefty since he was left-handed himself.
Many fans have tried to reason with the inconsistency of the character by saying that Link is ambidextrous. It cloud also be that, as character who constantly reincarnates, different incarnations have different dominant hands.
Some hope in the next game in the series that Link will return to his roots as the most popular lefty in video games.