Matt 11:16-19 is a brief parabolic take on how people responded to John the Baptist and Jesus, two prophets with two very different portfolios.
We are to imagine girls with flutes inviting boys to dance a wedding dance, and to imagine boys calling girls to sing a funeral dirge. But the boys do not respond to the flutes, or the girls to the wailing.
Many readers, supposing that the children represent John and Jesus, draw this analogy: John called for mourning and repentance in the face of judgment whereas Jesus proclaimed joy because of the presence of the kingdom, and in both cases their messages encountered unbelief or indifference. Other readers, observing that 11:16 likens "this generation" to those who play and wail, suppose that the piping and wailing children represent the disagreeable contemporaries of John and Jesus. When the Baptist came neither eating nor drinking but demanding repentance, people instead wanted to make merry: "We played the flute for you, and you did not dance." When Jesus came, preaching good news and celebrating, people demanded that he fast: "We wailed, and you did not mourn" (cf. Matt 9:14-17).
It is hardly possible to decide with confidence which of these two interpretations is the better. But whichever one we opt for, there is one constant: God's appeal came to the Jewish people of the first century in at least two diverse ways.
In this lies a lesson for us. We may sometimes be tempted to suppose that God is at work primarily or even exclusively in those who look like us. In the present text, however, God is at work in John and Jesus, and they did not look like each other. The two men had different ministries with different emphases. One celebrated the kingdom by eating and drinking at table; the other chose an ascetical lifestyle out in the wilderness. The differences between the two were indeed so great that John could wonder whether Jesus was really the one his inspired imagination had foreseen (Matt 11:2-4). And yet the same God was after all active in both.
The circumstance reflects the largesse of God, who meets human diversity with divine diversity. That is, because people are different, effectively communicating with them requires more than one approach, which means more than one speaker or one sort of speaker. The disparate ministries of John and Jesus are cause for us to recognize that whatever ministry we have can never be comprehensive or meet the needs of everyone. We will not reach all, and so we must respect and be generous toward those with the ability to reach people who will forever remain deaf to us. Instead of presumptuously and vainly imagining that what we say and do should be sufficient for all, we should rather be confident that God will raise up voices other than our own, voices for different ears with their different needs. As John and Jesus show us, there is more than one means to the great end that is God.
If the tone of 11:16-19, which analyzes the response of "this generation," is negative, the tone of 11:25-30, which concerns the "infants" who receive the divine revelation in Jesus, is positive. The passage has a specific background in the Old Testament. The declaration that the Father and the Son know each other in an exclusive fashion harkens back to Exodus 33, where God knows Moses and Moses prays that he might know God. In the Exodus passage, we also find the promise of rest (Exod 33:14: "I will give you rest"). Moreover, in deeming himself to be "gentle" (v. 29), Jesus is taking up a chief characteristic of Moses (see Num 12:3), and in speaking of his "yoke" (v. 29), Jesus is using a term often applied to the law given through Moses. So Matt 11:25-30, like so much of Matthew, presents the second redeemer, Jesus, as being like the first redeemer, Moses.
Matt 11:25-26 is first of all a Christological treasure. It reveals that Jesus is the revealer, it teaches that he is the source of spiritual rest, and it tells us that he is humble and gentle. But Christology cannot be reduced to doctrine, or to facts about Jesus. It is rather an invitation to redirect our lives. When Jesus says, "learn from me," he is calling us not just to read further in the Gospel or to mull over theological ideas but to incarnate for ourselves the virtues demanded by his speech and exhibited in his actions. One learns of Jesus by doing, by adopting his spirit and living his imperatives. The truth of our Christological faith is in the living. To read about feeding the hungry is one thing; to feed them is quite another. As 28:16-20 has it, disciples are "to obey," that is, to do what Jesus has commanded.
Among the characteristics of Jesus in this passage is his being "gentle" or, as the older translations had it, "meek." Exactly what this means here and in the beatitude in 5:5 ("Blessed are the meek, for they will inherit the earth") has been much discussed, especially among modern commentators, for whom "meek" sounds like such a bad thing. Who wants to be timid or ineffectual or of weak character? But it is crucial to observe that Jesus, who exemplifies this virtue according to 11:29 and 21:5, is very far from being a doormat. He enters into arguments, speaks harshly about opponents, and overturns the tables of the money changers in the temple. So whatever exactly this sort of humility may require, it cannot mean, without further ado, submissiveness or lack of spirit.