There is no scriptural support for this specific date being Jesus’ birthday. The date really comes from researcher Hippolytus of Rome, who decided it right off the bat in the third century, accepting that the conception of Jesus occurred at the Spring equinox, which he put on March 25. He at that point added nine months, taking advantage winter celebrations that were at that point celebrated around that time.
There are various blunders in this thinking, the least of which is that the human incubation cycle is really 40 weeks, which would put Jesus’birth at some point in mid-January. That, yet Luke makes a particular reference to shepherds grazing their sheep in the fields, which occurred distinctly in the hotter months of the year. December 25 wasn’t celebrated as Christmas until in any event the fourth century CE, when it turned into a vehicle to hinder Christians from praising the agnostic winter solstice.