Our most significant source of information about Jesus Christ comes from Matthew, Mark, Luke, and John in the New Testament. Yet the four gospel accounts should not be taken as an exhaustive narrative of the life and work of Jesus. John, for example, explicitly states that his account does not contain everything Jesus did (John 21:25).
Instead, the four writers had a specific audience in mind to address a defined issue. To that end, each one selected and arranged the factual historical data of Jesus's life in a way best suited for their chosen aim. Chronology and exhaustive coverage of specific events was secondary. However, this does not negate the guiding hand of the Holy Spirit in shaping and directing the writers of the gospels through divine inspiration.
Because the gospels serve more as Spirit-drawn narrative portraits, any "harmonizing" of the four accounts falls to the student of the Bible. Weaving the gospels together is possible, but the gospels should never be taken as an exhaustive biography in the modern sense. Instead, the accounts follow the common ancient method of highlighting key events and themes. Each telling presents a distinct perspective on the same life.
Matthew: Christ is the Son of David, rightful heir to the Messianic throne. Here we see Christ's royal genealogy, the visit by the magi from the East to announce His kingly birth, and the proclamation of His laws in the Sermon on the Mount.
Mark: Here we find Jesus as the Servant of God. Although Jesus came as God to earth, He completely submitted Himself to the will of the Father in heaven and took on the form of a servant. Anything extraneous to that theme is excluded, which is why the narrative contains no references to Jesus's birth or youth.
Luke: To Luke, Jesus is the Son of Man—fully human but unlike any other human being in His perfect submission to God's will. For this reason, Luke traces the genealogy back to Adam (the first human).
John: John presents Jesus as the Son of God—fully divine. Jesus is not only flesh and bones, but He is also the Creator of all things in the beginning (John 1). Jesus reveals His nature as "I am," a title God gave as His own.
In many cases, claims concerning the "contradictions" between the gospels ignore the different purposes of the four writers. The focus helps us understand what each intended to emphasize in the character of Christ. One account could never capture the complete picture.
~A. W. Pink~