Why the 25th?

It is generally accepted that Christmas was attached to the winter solstice.

So, why the 25th? Why not the 21st?

It is possible that the high priests and shamans among our early ancestors were unable to pin down the exact turn-around of the season. It probably took them about five days before they could say for sure that Hey! the sun is coming back.

That gave them something to celebrate and worthy of having the birth of Jesus Christ attached to that date. That's good thinking on the part of Christianity's early spin doctors.