It is of course about human modesty, as Cynthia Avishegnath (+1) is saying, yet this dialogue as told in Matthew 3:13-15 appears to be a very difficult place. John's baptism is a penitential practice. John recognizes himself as a sinner and Jesus as without a sin. A sinner can not clean up a sinless person. This is more than human modesty. There were several attempts to address this issue even since the 4th-5th century. Please find below some fragments from those ancient commentators. The 2nd and the 3rd are not directly answering the question, however they kind of getting you out there. I'll just let them speak for themselves:
The human modesty meaning:
Origen (3rd century), Fragment 52:
By this act Jesus showed himself to be “meek and lowly in heart” (Mt 11:29), coming to those inferior to him, doing all that followed in order to humble himself and become obedient “unto death” (Phil 2:8). It is not always the case that the one who baptizes is greater than the one who is baptized. Ananias was not greater than Paul (Acts 9:10–18). And while Philip baptized (Acts 8:13, 38), Peter gave the Spirit through the laying on of hands.
The 2nd and the 3rd are not directly answering the question:
Hilary of Poitiers (4th century), Homilies on Matthew, 2.5:
In Jesus Christ we behold a complete man. Thus in obedience to the Holy Spirit the body he assumed fulfilled in him every sacrament of our salvation. He came therefore to John, born of a woman (see Gal 4:4), bound to the law and made flesh through the Word (see Jn 1:14). Therefore there was no need for him to be baptized, because it was said of him: “He committed no sin.” (1 Pet 2:22) And where there is no sin, the remission of it is superfluous. It was not because Christ had a need that he took a body and a name from our creation. He had no need for baptism. Rather, through him the cleansing act was sanctified to become the waters of our immersion.
Jerome (4th-5th), Commentary on Matthew, 1.3.13:
For three reasons the Savior accepted baptism from John. First, because he was born a man, that he might fulfill all justice and humility of the law. Second, that by his baptism he might confirm John’s baptism. And third, that by sanctifying the waters of the Jordan through the descent of the dove, he might show the Holy Spirit’s advent in the baptism of believers.
The next two are very interesting:
John Chrysostom, Homilies on Matthew, 12.1:
John’s baptism was looking toward repentance. Its purpose was to bring hearers to the point of experiencing conviction for their offenses. John, however, did not want anyone to draw the conclusion that Jesus himself also came to the Jordan to repent of his sins. So he sets this point straight from the outset by calling him both Lamb and Redeemer of all the sin that is in the world. He who is able to take away the sins of the whole world was himself without sin.
Chromatius of Aquileia (cca 5th), Tractate on Matthew, 12.1; 13.2-3:
Jesus therefore descended to fulfill all the observances of the law, and in this context he was baptized by John in Galilee at the Jordan. But John, recognizing the Lord as his God through the Holy Spirit, declared that he was unworthy to bear his sandals. He excused himself from doing what he was directed to do, because he could not conceive that baptism was necessary for the One whom he knew had come to blot out the sins of the world. He rather pled that he himself ought to be baptized by Christ, saying, “It is I who should be baptized by you, and do you come to me?” It is as if he were saying, “I am a man. You are God. I am a sinner because I am a man. You are sinless because you are God. Why do you want to be baptized by me? I do not refuse the respect you pay me, but I am ignorant of the mystery. I baptize sinners in repentance. But you have no taint of sin. So why do you want to be baptized? Why do you want to be baptized as a sinner, who came to forgive sins?” This is what John in effect was saying to the Lord. [...] The Lord here is testing the faithful deference of service on the part of his servant, but he reveals the mystery of his dispensation by saying, “Let it be so now; for thus it is fitting for us to fulfill all righteousness,” showing this to be true righteousness, that he the Lord and Master should fulfill in himself every sacrament of our salvation. Therefore the Lord did not want to be baptized for his own sake but for ours, in order to fulfill all righteousness. Indeed, it is only right that whatever someone instructs another to do, he should first do himself. Since the Lord and Master of the human race had come, he wanted to teach by his example what must be done for disciples to follow their Master and for servants their Lord.