1. In Matthew 21:23-27 Jesus is asked about his own authority by none other than the “chief priests and the elders of the people.” Jesus replies by asking if the baptism of John was from heaven. This is an odd question if it could simply be settled by asserting John’s birthright to the Aaronic priesthood.
2. Jesus saw himself as above the priests of Aaron and the temple priesthood system. In Matthew 12:1-8 Jesus likens himself to David, who had, as the Anointed King, implicit authorization to enter the temple — something otherwise expressly prohibited. David “entered the house of God and ate the bread of the Presence, which it was not lawful for him to eat nor for those who were with him, but only for the priests.” (12:4) In verse 6 he says, “I tell you, something greater than the temple is here.” Implicit: Something greater than the priesthood is here. Move along, Pharisees. The boss of the temple is here and he is also boss of the Sabbath.
3. In the Gospel of Matthew Jesus’ whole life is seen as a giant parable. He is the Immanuel born of a virgin (1:23). He is the Son who travels to Egypt and is called out of Egypt (2:15; think of Abraham and Israel). He is the one over whom the wicked leader kills the baby boys (Matthew 2:16-18; in addition to fulfilling Jeremiah 31:15, this reminds us of Exodus 1:22). He grows up in Nazareth to fulfill the words of the prophets (Matthew 2:23). The flow of Jesus’ pre-ministry life smells like the Old Testament.
4. In addition to literally smelling, John’s life parabolically smells like the Old Testament too. He ate bugs and wore an “Elijah custume” , with “a garment of camel’s hair and a leather belt around his waist.” (Matthew 3:4) Jesus confirms that John was the Elijah to come:
> “‘Elijah does come, and he will restore all things. But I tell you that Elijah has already come, and they did not recognize him, but did to him whatever they pleased. So also the Son of Man will certainly suffer at their hands.’ Then the disciples understood that he was speaking to them of John the Baptist.” (Matthew 17:11-13)
John had jettisoned Jerusalem and went “back” to the Jordan River and the desert, showing he believed the Jews were still wandering and needed another “circumcision.” This reminds us of when Joshua led the Israelites out of the wilderness across the Jordan River to begin the conquest. After a generation of rebellion, Israel’s re-circumcision was a sign of repentance and covenant-renewal. John the Baptist’s baptism of repentance at the Jordan River is no coincidence. Instead of doing baptism near the temple under the direction of the priesthood regime, John was spurning the temple/priesthood regime and ushering the arrival of the kingdom with repentance.
5. John the Baptist tells us why he ultimately baptized, and that is to reveal Jesus to Israel:
> “I myself did not know him, but for this purpose I came baptizing with water, that he might be revealed to Israel.’ And John bore witness: ‘I saw the Spirit descend from heaven like a dove, and it remained on him. I myself did not know him, but he who sent me to baptize with water said to me, ‘He on whom you see the Spirit descend and remain, this is he who baptizes with the Holy Spirit.’” (John 1:31-33)
6. John himself thought the baptism should have been reversed! (Matthew 3:13-17) “I need to be baptized by you, and do you come to me?” Jesus insisted, wanting to fulfill all righteousness. This insistence is humble, because the baptism is otherwise a baptism of repentance. Jesus didn’t need to repent. And it certainly wasn’t clear to John that Jesus needed John’s authority. If anything, John felt the opposite: “He who comes after me ranks before me, because he was before me!” (John 1:15)
Summary: Jesus saw himself as above the temple priesthood system, was fulfilling a parabolic life, was intersecting with John’s parabolic life, was illustrating humility, was revealing himself to Israel through John, was honoring John as the promised Elijah to come, was endorsing John’s rejection of the temple/priesthood regime, and was endorsing his ministry of repentance. He was fulfilling all righteousness. He was not, however, receiving or depending on authority from another human being.
 I love this phrase. I got it from my friend Ariel.
 Thanks to Jeff for pointing this out to me
Addendum: Craig S. Keener on the baptism of Jesus and his “fulfill[ing] all righteousness”:
> John’s location suggests that the biblical prophets’ promise of a new exodus was about to take place in Jesus. So significant is the wilderness (3:1) to John’s mission that all four Gospels justify it from Scripture (3:3; Mk 1:3; Lk 3:4); some even suspect that John himself used this text (Is 40:3) to explain his own sense of mission (Jn 1:23; Robinson 1962: 13). The meaning of John’s location would not be lost on Syro-Palestinian Jews. Israel’s prophets had predicted a new exodus in the wilderness (Hos 2:14–15; Is 40:3; later interpreters properly understood such passages as applicable to the time of Israel’s restoration—e.g., Ps. Sol. 11:1)…
> Although Jesus alone did not need John’s baptism—he was the giver of the true baptism (3:11)—he submitted to it to fulfill God’s plan (3:14–15). In a traditional Mediterranean culture where society stressed honor and shame, Jesus relinquishes his rightful honor to embrace others’ shame. After Jesus’ public act of humility, God publicly identified Jesus as his own son (3:16–17; cf. 2:15)—that is, as the mightier One whose coming to bestow the Spirit John had prophesied (3:11–12)…
> Jesus humbly identifies himself with John’s mission… Jesus “fulfills all righteousness” by identifying with his people (3:15)… Matthew’s readers familiar with the Scriptures would already understand that Jesus sometimes “fulfilled” the prophetic Scriptures by identifying with Israel’s history and completing Israel’s mission (2:15, 18). This baptism hence represents Jesus’ ultimate identification with Israel at the climactic stage in her history: confessing her sins to prepare for the kingdom (3:2, 6). Jesus’ baptism, like his impending death (cf. Mk 10:38–39 with Mk 14:23–24, 36), would be vicarious, embraced on behalf of others with whom the Father had called him to identify. This experience prepares Jesus for testing by the devil (4:1–11)—perhaps part of what it means for Jesus to fulfill all righteousness. No less plainly, this text makes Jesus an example of humility (cf. 11:29; 12:19; 21:5).”
Keener, C. S. (2009). The Gospel of Matthew: A Socio-Rhetorical Commentary (116–117, 131, 132). Grand Rapids, MI; Cambridge, U.K.: Wm. B. Eerdmans Publishing Co.