The received notion is that December 25th was chosen for the celebration of the birth of Christ to help convert pagans. But, the evidence for that idea is weak. A very interesting article in Biblical Archaeology Review gives another perspective. It concludes:
How did December 25 become Christmas? We cannot be entirely sure. Elements of the festival that developed from the fourth century until modern times may well derive from pagan traditions. Yet the actual date might really derive more from Judaism—from Jesus’ death at Passover, and from the rabbinic notion that great things might be expected, again and again, at the same time of the year—than from paganism.
The whole article “How December 25 became Christmas” here.