From your own sources:

"Though December 25 is the day Christians celebrate the birth of Jesus Christ, the date itself and several of the customs we've come to associate with Christmas actually evolved from pagan traditions celebrating the winter solstice."

"It's a mistake to say that our modern Christmas traditions come directly from pre-Christian paganism, said Ronald Hutton, a historian at Bristol University in the United Kingdom. However, he said, you'd be equally wrong to believe that Christmas is a modern phenomenon."

"Christmas, Christian festival celebrating the birth of Jesus."

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Like I said, certain traditions were stolen and incorporated. No one is denying that. However, Christians celebrated the birth of Christ well before those pagan traditions were incorporated into the celebrations. This is all well detailed in the wiki article I linked, chock full of academic sources. It is also fully acknowledged in all of the sources you provided, which, to be honest, I'm not sure you've actually read beyond the headline.

I am sorry that you are incapable of admitting that you are wrong, or of understanding nuance, and that you care more about your own pride than the historical accuracy of your statements, but to each their own. I'm gonna move on because like most people in these threads, I'm done reading your ignorant contrarian takes.