Because they were awed by their special view of God's creation. For Christians (and many others) this would immediately spring to mind. It is also one of the most well-known parts of the Bible, whether one reads it often or not. Because it was at Christmastime, the astronauts wanted to read something special and inspirational. See this from wikipedia:
"After launching on December 21, 1968, the crew took three days to travel to the Moon. They orbited ten times over the course of 20 hours, during which the crew made a Christmas Eve television broadcast in which they read the first 10 verses from the Book of Genesis. The crew timed this reading to coincide with a full view of planet Earth hanging in the empty blackness of space while clearly showing the rich diversity of the living planet as indicated in Earth's colors, seas, landforms, and weather patterns, rising over the dull gray horizon of the lifeless Moon."
- For Teachers