Around this time of year the careless and unobservant (and those incapable of reading simple Greek) like to ‘point out’ the ‘contradictions’ between Matthew and Luke in their telling the story of the birth of Jesus. So let me set them straight: there are no contradictions. Why? Because, simply put, Matthew and Luke are talking about different periods of time.
Luke tells the story of Jesus’s actual birth. He is born in Bethlehem, laid in a stable, and is visited by shepherds. He is, in Luke’s telling, a newborn infant. Here’s Luke’s bit-
While they were there, the days were completed for her to give birth. And she gave birth to her firstborn son; and she wrapped Him in cloths, and laid Him in a manger, because there was no room for them in the inn. In the same region there were some shepherds staying out in the fields and keeping watch over their flock by night. And an angel of the Lord suddenly stood before them, and the glory of the Lord shone around them; and they were terribly frightened. But the angel said to them, “Do not be afraid; for behold, I bring you good news of great joy which will be for all the people; for today in the city of David there has been born for you a Savior, who is Christ the Lord. “This will be a sign for you: you will find a baby (βρέφος) wrapped in cloths and lying in a manger.” And suddenly there appeared with the angel a multitude of the heavenly host praising God and saying, “Glory to God in the highest, And on earth peace among men with whom He is pleased.” (Lk. 2:6-14)
Luke chooses his words quite carefully, including the word translated ‘baby’, βρέφος. This is the Greek word for newborn.
Matthew says nothing about shepherds because, frankly, he doesn’t care about shepherds. He is far more interested in talking about a few years later, when wise men arrive from the east, after having seen a star appear announcing the birth of the promised Messiah. Their journey takes time, so when they arrive, they find Jesus and his parents not in a stable, but in a house. And the child is no longer a βρέφος, he is a παιδίον. This is not the same word Luke uses and it doesn’t describe a newborn, it describes a child, a toddler. Here’s Matthew:
Entering the house, they saw the child (παιδίον) with Mary His mother, and falling to their knees, they worshiped Him. Then they opened their treasures and presented Him with gifts: gold, frankincense, and myrrh. And being warned in a dream not to go back to Herod, they returned to their own country by another route. (Matt. 2:11-12)
The conflation of Matthew with Luke is a modern invention. The shepherds and the wise men were not at Jesus’s birth together, at the same time, as portrayed in the usual nativity play. They were separated by a couple of years. Furthermore, Matthew and Luke aren’t talking about the same period of time and accordingly they are not ‘contradicting’ each other any more than you contradict yourself when you say you ate eggs and that you ate a burrito if you ate eggs for breakfast and a burrito for dinner.