"Son" and "sun" is an English homophone that has zero application to Christmas. The winter solstice varies but its most common day is the 21st. You are basically repeating bad arguments from atheists and Jews. There was nothing pagan when Christians were debating the day Christ was born, and they settled on celebrating the 25th of December.
It has a mishmash of traditions because you have a mishmash of cultures that formed the base of the Christian peoples of Europe.
Yet there are many traditions which are fundamentally Christian that are accused to have predated it. The Christmas tree one of them, when it's origin was not some pagan ritual, but a medieval play where the tree of life was that of a fir tree decorated with apples. Whereas lighting the Christmas tree with candles came from Martin Luther.
Why? Because the fir tree is often associated with eternal life. It's a symbol for the redemption of the house of Israel.
Ephraim shall say, What is it to me any more with idols? I answered him, and I regarded him. I am as a green cypress tree; your fruit is found from Me.
How much do you actually know about the various traditions we hold and where they come from? The fact is, when it comes to God and what He holds sacred and us, it blends together. Which often means we misuse things. Look at the zodiac, all of those signs were placed by God, but now pagans decide your personality based on them.
who made the Bear, Orion, and Pleiades, and the chambers of the south;
He who created the Pleiades and Orion, and turns the deep darkness into the morning, and He darkened the day into night; who calls for the waters of the sea and pours them out on the face of the earth, Jehovah is His name;