Today, we can see that, besides fasting on the Day of Atonement (cf. Lev 16:29-34), the Jewish people observe many other days of fasting, both public and private. Days of fast manifested mourning, penance, purification, preparation for a feast or a mission, demand of God's grace, etc. Pious Jews considered fasting an act of virtue of their religion which pleased God. One who fasts addresses God in an attitude of humility; he implores forgiveness for his separation from God while depriving himself of those things that often cause the separation.
That Jesus does not instill this practice into his disciples and followers comes as a surprise for John's disciples and for the Pharisees. They cannot understand it. But Jesus gives them a fundamental reason: «How can the wedding guests fast while the bridegroom is with them?» (Mk 2:19). For Israel's prophets, the bridegroom signifies God himself, faithful Yahweh, and his divine love for men (in contrast to Israel, his not always so faithful spouse). Hence, Jesus is tantamount to Yahweh, and He here declares his divinity: he calls his disciples «the bridegroom's friends», and those who are with him do not need to fast for they are not separated from him.
The Church has remained faithful to Christ's teaching on fasting which, though coming from the prophets and even being a natural and spontaneous practice in many religions, our Lord confirms with a new meaning. Fasting can be used as preparation; it strengthens prayer and contemplation. Jesus fasts in the desert as a preparation for his public life.
Many poor people, not unacquainted with shabby clothes were among those who listened to our Lord. So too were vintners who certainly knew what happens when the new wine is put into old wineskins. Jesus reminds them all that they have to receive his message with a new spirit, one that breaks with conformity and the routines of jaded souls; Jesus proposes something entirely different, not another version of the Law, but a new life altogether.