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J_Edwards said:

Is not the day they selected (25 Dec) in the mid 300's associated with the birth of Mithra (alluded to in Ezra 1:8, 4:7) and associated with a pagan ritual ?

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Mithra (app. 2500 years before the birth of Christ)

This god is said to have been born in a cave where shepherds came to worship him, believing him to be a son of god. His birthday was celebrated each year on December 25th. He was believed to have been killed by the god of darkness but had later risen from the dead. His resurrection was celebrated each year in the early spring. In observance of this, a white bull or lamb was slain over a metal grating. Underneath the grating, blood from the lamb dripped down and "baptized" new converts who would join Mithra in the eternal war against evil. His followers then ate bread and wine in a mass communion meal. Mithraism and Christianity

Also you should wonder why they picked a date which was after shepards came back from the fields with the flocks. Why pick a date with pagan roots unless you want to appease the pagans.