In fact, I do.
Christmas is indeed on the same day as the ancient pagan holiday, as you mentioned. Thank you for the time and thought you put into your message.
However, Christmas as we know it is not that holiday. It was actually a rival holiday put on the same day, partly in order to do what you just mentioned, to bring converts over.
The only difference is, while the ancient gods of antiquity are all but forgotten, we are reminded each year of how God invaded time and sent His Son into a very dark world to be the Light that guides us all Home.
So, Christmas, while it isn't the actual chronological birth date of our Lord Jesus, it was moved there on purpose. T
oday, when people think of Christmas, most do not think pagan worship, they think of the birth of our Lord.
Merry Christmas back atcha.