None of the gospels are historical records like the Jehovah's Witnesses or the Fundamentalist Christians teach. Each is a catechesis built upon the Gospel message that was being preached by the Christians. Regardless of what you may have learned from the Watchtower, the Gospels don't agree becuase simply they are not supposed to.
The first account and the simplest is the Petrine Gospel. Composed by Mark, a non-apostle, because of its Petrine source the composition became the basis for Luke and the finalized version of Matthew. Mark is the primitive account, written simply to impress the Christian view that the Passion of Christ was a victory and not a defeat.
The Matthean account is based on a sayings gospel (tradition holds that the oracles are those spoken of by Papias and may even be the theorized Q), and is a catechesis for Jewish Christians. It is designed not in chronilogical order like Mark, but in in order of five lessons to impress upon Jews that Jesus is the Messiah that Israel has been waiting for. The five sections are meant to copy the five Books of Moses. This gospel relies heavily on midrash, a Jewish form of exegesis to "prove" Jesus is he Messiah of Hebrew Scripture.
Luke's account is a Gentile catechesis, meant to impress the universality of Jesus. Written in the style of a lesson to a Gentile who has converted to Judaism, Luke also builds on Mark, employing a chronilogical and very precise order to show that Jesus is the Savior not only of the Jews but of the world.
None of are meant to be history. The Jehovah's Witness theology on this point is contrived on the Gnostic belief that a written text is a greater revelation from a divine source than anything. In reality Christianity is based on a person, Jesus of Nazareth, and the confession of the college of apostles. Each gospel is merely a different tool used to spread this witness in catechism form. Like all catechisms, each is adjusted for the culture and audience it is designed for. The synoptic gospels are catechisms.
The gospel of John is a late testimony, not so much catechesis as it is reflection and theology based on the gospel message. It uses none of the earlier sources because it's intention is exegesis, explain what Jesus means and why this meaning should convince an audience in the face of the growing threat from Gnosticism and other worldly philosophies.
One has to let go of the Watchtower views which demand the gospels are historical accounts, even those who become agnostic or atheist. It is the earmark of academic ignorance to claim that these books were even intended to be read like history.
Regardles if Jesus was real, regardless of what he spoke, one should not fan the flames of Watchtower/Fundamentalism ignorance by advancing the equally contrived in order to disprove straw man claims.