The historical death and resurrection of Jesus of Nazareth is, by the standards of the day, extremely well documented, widely witnessed, and reliable. The birth narratives are not.
The birth narratives consist of after-the-fact God-hero mythology added by the Gospel writers to communicate the deity of Christ to their own generation.
The celebration of Christmas derives from the Bishops of Rome co-opting the Roman feast of Saturnalia in order to give the people an alternative festival. It is neither Scriptural, historically based, nor universally observed within Christianity (e.g., the Presbyterian Reformed Church).