Summary: 1) A Critical Accusation (Mark 2:18), 2) A Corrective Answer (Mark 2:19-20), 3) The Clarifying Analogies (Mark 2:21-22)
The Jewish New Year 5774 began this year on the evening of September 4th. Ten days later, just before sundown on September 13th, Jews worldwide gather in their homes to eat a final meal together before they embark upon a 25-hour period of fasting and prayer on the holiest, most solemn day of the Jewish year - Yom Kippur, the day of atonement.
In Mark 2, Jesus and his disciples had just come from the feast in Levi’s house, and this seems to have been a day when the disciples of John thought that they had to fast, and the scribes likewise (Lenski, R. C. H. (1961). The Interpretation of St. Mark’s Gospel (pp. 118–119). Minneapolis, MN: Augsburg Publishing House.)
Given the practices of Jesus, and the times where some fast and some do not, how do we decide when or if to fast? Should it be on regular intervals, or special occasions?
Jesus is going to answer these questions in the context of the Gospel and New Covenant itself. In this answer, he is going to explain the purpose of fasting and the nature of His atonement. The fast in Mark 2, provides an opportunity to show how the old covenant fast is now fulfilled in Christ and his atonement, and how fasting now remembers that atonement. He shows this through:
Jesus is presented with the opportunity to clarify the purpose of fasting, first through:
1) A Critical Accusation (Mark 2:18)
Mark 2:18 Now John's disciples and the Pharisees were fasting. And people came and said to him, "Why do John's disciples and the disciples of the Pharisees fast, but your disciples do not fast?" (ESV)
Aside from this passage and its parallels in Matt 9:14–17 and Luke 5:33–39, the New Testament says little about fasting. The only passages are Matt 6:16–18; Acts 9:9; 13:2–3; and 14:23. Fasting is a matter of Christian freedom, not obligation. On some occasions fasting is inappropriate, and on others it is appropriate. The nearness of the kingdom of God in the person of Jesus was not a fitting time. During his absence fasting may be desirable. (Brooks, J. A. (1991). Mark (Vol. 23, p. 64). Nashville: Broadman & Holman Publishers.).
For the situation in verse 18, the topic of fasting is the context of the exclusivity of the gospel, about the incompatibility with the gospel, the inability of the message of Jesus Christ to be mixed with apostate Judaism or any other false religion.
Frequently, conflict with Jesus and the leaders of Israel, the Pharisees and the scribes, is built around questions. Those questions seem most of the time to have to do with Jesus' contrary behavior. Either He's violating one of their laws, traditions, or He's doing something on the Sabbath that, in their minds, He shouldn't be doing, or there's some behavior in which His disciples are engaged, which is a breech of their tradition. This launches the conflict, and that is the case here.