Christmas is celebrated as the birthday of Jesus but its NOT THE BIRTHDAY OF JESUS.
As per Bible records, when Jesus had taken birth, the shepherds were out in the night with their sheep when the angel appeared to them telling them about the birth of Jesus. Please note, December is a winter month and at that time its impossible to stay outside in Bethlehem (the place where Jesus was born), as it snows heavily. So, we can conclude that Jesus has not taken birth on Dec 25th.
Then when did Jesus take birth. Bible gives the answer. Though it doesnt tell the exact date of birth, it does tell the date of death of Jesus, i.e. 14th of Nisan month. And it also tells that Jesus lived for 33 and a half year. So, if we count backwards, it comes to around the month of October. Though we cant say the exact date.
Then why does the world celebrate Jesus' birthday as Christmas on Dec 25th. In ancient pagan times, the last day of winter in the Northern Hemisphere was celebrated as the night that the Great Mother Goddess gives birth to the baby Sun God. In Roman times, it became the celebrations honouring Saturnus (the harvest god) and Mithras (the ancient god of light), a form of sun worship. To avoid persecution during Roman Pagan festivals, christians started observing this festival. But please note that the early christians didnot celebrate the birth of Jesus. In 325AD, Constantine the Great, the first Christian Roman emperor, introduced December 25th as Christmas. In 354AD, Bishop Liberius of Rome officially ordered his members to celebrate the birth of Jesus on 25 December.