And when they had performed everything according to the Law of the Lord, they returned into Galilee, to their own town of Nazareth.
If a casual reader of the bible were to first read the birth account of Jesus Christ in the Gospel of Matthew, and then read the birth account in the Gospel of Luke, the following questions might pop in that reader's head about Luke's account:
"Where is the visit of the Magi?"
"Where is the slaughter of the innocent?"
"What about Joseph, Mary and Jesus going down to Egypt?"
Our proposed reader might then make the conclusion that since these events are omitted from the account recorded by Dr. Luke, then that means that there are contradictions in the two recorded accounts (e.i. Matthew and Luke). That is the conclusion that many who reject the Bible as a whole come to. As a matter of fact, some Biblical skeptics have made a career out of claiming such things.
Bart Ehrman, a New Testament scholar, and currently the James A Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill, has made a very lucrative career out of claiming that the Bible is full contradictions and major errors in the early manuscripts that we still have today. To be honest, most of the "errors" in the manuscripts that Ehrman likes to point out are mostly things like minor differences in the spelling in the different manuscripts, and many of the others have been addressed and explained many years ago by Christian Biblical scholars who were more reputable that Dr. Ehrman.
Now to the differences in the birth accounts recorded in the Gospels of Matthew and Luke. First of all, let's understand that all four Gospel (i.e. Matthew, Mark, Luke, John) were each written with different original audiences in mind. Each Gospel emphasized on different aspects of the life and ministry of the Lord Jesus Christ.
Each of the four Gospels are like different sides of the same diamond. Each has a different sparkle to it, but it is part of the same diamond.
Most importantly, all four Gospels, just like the rest of the Bible, were inspired by the third person of the Trinity, the Holy Spirit. ( c.f. 2 Timothy 3:16). The Holy Spirit does not make any contradictions or mistake.
Let the Scriptures defend itself. Let Scriptures explain Scripture, and used the clearer portions of Scripture to interpret the more difficult portions of Scriptures.
"Scriptura Scripturam" (Scripture interprets Scripture) was the believe and practice of Luther, Calvin, and many of the sixteenth century reformers. It has been the belief and practice of all true believers throughout the history of the church, and it should be of ours today.