Apparently the date of December 25th was settled on primarily because it was longest night (or, considering the primitive time keeping equipment then existing, was mistakenly thought to be the longest night) and it seemed that all the Gospel events that apparently took place at night would have needed as much time as possible to unfold.
Whether Dec 25th was chosen because it was already being used by various pagans is debatable, but it is certain that a lot of pagan cultures had already noticed that the longest night was on or around Dec 25th and were marking that night in various ways.
Another possible reason for picking Dec 25th, or while that date might have prevailed over other candidate dates, is that it comes in the midst of winter. In a pre-industrial age the vast majority of the population in Europe would have dug themselves in as the snows began in November or October, resigned to see no one outside the household and eat nothing but stored roots until the spring thaw; celebrating Christmas on Dec 25th gave them an opportunity and excuse to dig themselves out, socialize and have some amusement midway through this hibernation.
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