It is difficult to know why God chose to have only four gospels written instead of two, six, or even twelve. The Bible also does not reveal why only two of the writers were among Jesus' original twelve disciples (Matthew and John) and the other two were not (Mark and Luke). One factor may be that Matthew and John, based on natural talents and education, were the best gospel writers using the Greek language.
For special tasks, like the writing of the gospels, God seems to work with people (e.g. Moses, Paul, etc.) who already have certain natural talents and abilities before he calls them. It could also be that it was not necessary to have more than four testimonies since they cover perfectly the different shifts in perspective of Jesus' ministry.
Early Catholic writers noticed the variations in the gospels concerning their portrayal of Jesus. Each of the four writers has a different emphasis concerning Jesus' ministry and a different specific target audience of would-be readers for their book. The Holy Spirit guided each of them when they wrote so that none of them recorded historical errors or contradictions.
The variations among the gospel writers, such as various events included or deleted, relate to what theme or focus the writer of a particular book desired. It is like, as Gleason Archer states in his book "Encyclopedia of Bible Difficulties," a camera taking different pictures from a variety of angles of the same room. Each view is correct, but some shots omit detail that others include.
The focus of each book
It is a bit of a mystery why Matthew organized his book, apart from the other gospels, with five divisions. Each division begins with a similar phrase followed by one of Christ's speeches, which each state something about the kingdom of heaven.
Now it came to pass that when Jesus had finished these words (Matthew 7:28, HBFV throughout)
And it came to pass that, when Jesus had finished commanding His twelve disciples (11:1)
And it came to pass that when Jesus had finished these parables (13:53)
And it came to pass that when Jesus had finished these sayings (19:1)
Now it came to pass that when Jesus had finished all these sayings (26:1)
One interesting theory is that Matthew was trying to divide His book by five in order to correspond with the first five books of the Bible (known as the Torah). This is an ancient idea, going back to the first and second century Christian writer Papias.
After all, Matthew was specifically targeting a Jewish audience more than the other three Gospels, so he may have wanted to make his book correspond with the Pentateuch. This idea makes a certain amount of sense since he wrote the first of the four gospels (in 35 A.D.), just as the Torah was the first section of the Old Testament.
One scholar, Frederick Grant, pointed out that the Psalms has five divisions and that the "Megilloth" (the five books of Ruth, Ecclesiastes, Song of Songs, Lamentations, and Esther) is a set of five as well. Perhaps Matthew, as a Jew writing to a Jewish audience, simply felt five pieces to his gospel account was a good or "Jewish" organizing principle for a historical document about the Messiah.
The gospel of Matthew itself strongly emphasizes Jesus' role as the Messiah who fulfills various Old Testament prophecies. Its perspective is different from that of Luke, who was a gentile writing to a more general audience. For example, Matthew traces Jesus' ancestry from Abraham, the ultimate ancestor of the chosen people (Israelites). Luke, however, traces Jesus' genealogy back to Adam, the ultimate father of all humans.
Mark's gospel (which church tradition states was heavily influenced by Peter's perspective) is also aimed at gentiles, with a particular emphasis on the Romans. Its focus is on Jesus as a powerful miracle worker, and as someone who conquered Satan, sickness, sin, and even death. Mark portrays Jesus as a man of action compared to His role as a teacher.
Luke is more systematic in his writing, with an aim to record a universal history that is looser in chronological order than the other two Synoptic Gospels (Matthew and Mark). He uses Greek words not used elsewhere in the New Testament. He also seems to use more precise medical terms than the other writers do, no doubt due to his medical background. Luke also records more of the role of women in Christ's ministry than the others do.
John's book (the third of the four gospels written), emphasizes Jesus as both man and God. Much of this writing concerns Jesus' relationship with His Father and how one gains reliable spiritual knowledge about him. An argument can be made his book is for already converted Christians who have learned the basics about the story of Jesus and wish to go on to an advanced lesson.
A significant portion of John's gospel records teachings Christ reserved for only his closest disciples. For example, much of his book (from chapter 13 to 17) was spoken on the night of the Passover shortly before Christ died. His writing also gives the best general timeline of Jesus' ministry of all the gospels, since it mentions at least four separate Passover celebrations, pointing to the fact that Jesus' ministry lasted at least three years rather than just one.