Many societies have had a winter festival designed to give hope for the coming spring when all is dead and cold around them. Yes, Christmas was placed on December 25 because it was a popular time for a festival of hope for the coming year. The message of Christmas fits with the general theme of those winter festivals, all of which had religious origins. I note that you also wrote "the pagan holiday," as if there was only one. Sorry, the festivals to which Christmas was added had, at one time, usurped their date from some previous winter festival.
The question isn't who performed the first winter festival; that's lost in time and will never be known. But the opposition to Christmas isn't about sharing, it's about suppressing.