This line of thinking is a typical Watchtower exercise in leaps of logic.
When was Jesus born? No one knows. We don't even know if Jesus ever existed. Let's assume Jesus was born. Again we don't know when.
Is that sufficient reason not to celebrate Jesus' birth? That is to say, is that sufficient reason to believe the alleged Almighty God/YHWH of the Bible does not want the birth of His son on Earth celebrated? Is it a sin in itself to celebrate the birth of the Messiah? Short answer - No.
Many cultures in the past had celebrations during the winter solstice. These celebrations honored gods other than the God/YHWH of the Bible. At some point these cultures converted to Christianity. These cultures enjoyed their winter festivals, but wanted to honor Jesus rather than their old gods. The church sanctioned this.
Is the stopping of the honoring of old gods and starting of honoring Jesus a sin?
Now, some might argue that the Bible does not record any command to honor Jesus birth on Earth? The concept of "it must be in the Bible or it is false" was a heretical teaching of Martin Luther. It is known as Sola Scriptura or "By Scripture Alone". Luther's Reformation movement started in 1517, 1,484 years after Jesus' death and alleged resurrection. As early as 125 CE Christians were celebrating Jesus' birth.
I no longer believe in the Bible as a book of historical fact, the existence of the God of the Bible, or that the historical Jesus was immaculately conceived or the literal son of God. I do know that the Watchtower attack on Christmas is full of logical fallacy.