Why did the Prophet (peace be upon him) fast on the day of Ashura?

The Messenger of Allah, peace and blessings be upon him, encouraged fasting certain days of the year other than Ramadan, among them the day of 'Ashura. He, peace and blessings be upon him, fasted it because Musa (Moses), peace be upon him, used to fast it. It is the day Allah saved Musa from Pharaoh. Ibn Abbas narrated that the Prophet, peace and blessings be upon him, saw the Jews fasting on 'Ashura and asked, "What is this?" They said, "It is a righteous day, the day Allah saved Musa and the Children of Israel from their enemy, so Musa fasted it." The Prophet, peace and blessings be upon him, said, "We are more rightful to Musa than you," so he fasted it and commanded its fasting. And from Abu Musa Al-Ash'ari, on the day of 'Ashura, which the Jews honored and took as a feast, the Messenger of Allah, peace and blessings be upon him, said, "You [Muslims] fast it."