Eprom said:
The question I have is: Why was Jesus baptized by John and why did Jesus say it would fulfill all righteousness?
John's baptism was a baptism of repentence. But note the progression here.
Mark 1:4 John did baptize in the wilderness, and preach the baptism of repentance for (unto) the remission of sins.
Luke 3:3 And he came into all the country about Jordan, preaching the baptism of repentance for (unto) the remission of sins;
Acts 13:24 When John had first preached before his coming the baptism of repentance to all the people of Israel.
Acts 19:4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
The baptism was not simply to be sorry for sinning, nor to turn away from them in a strictly individual sense. It was the turning away from sin in totality and from the system of works theology because it could save no one from their sins.
Galatians 3:24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. 25 But after that faith is come, we are no longer under a schoolmaster.
Romans 3:31 Do we, then, nullify the law by this faith? Not at all! Rather, we uphold the law.
Jeremiah 31:31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: 32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: 33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. 34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
And John the Baptist was prparing the way for the Messiah who was bringing in the New Covenant.
So it was not just baptism to repent of sin, but of the futility of trying to save one's self and to emerge unto the New Covenant of God's total grace for faith in the Lamb of God sacrificed for the sins of the world.
Jesus submitted to the baptism of John not to repent of sin but of the Old Covenant system to usher in the New.