“I do not agree with what Shaikh Mashhor has said. His statement is false.”
In order to reject what he said you must have in-depth knowledge on the topic. In addition, not agreeing what was said does not mean that what he said was said in error.
“They believe that the origins of this holiday are authentic, and it is a religious symbol for them. How can one reject what is of their religious foundations”
No educated Christian believes in Christmas. The details of the birth of Christ are taken mainly from Mathew. This gospel is of unknown origins. We have yet to determine the date which it was actually written. While it is true that the majority have estimated that it was written between 80 & 90 AD. While many find similarities between Mathew & Mark and Luke, the reality is that this is not suffice to prove authenticity. Experts agree however that the author was of Hebrew origin. In conclusion to come after all of this and claim that Christmas is of a part of Christian foundation is very peculiar. And those that claim such atrocities must answer directly to the direct verses in the bible it self mention at the beginning of this response.
“How can he say that the origins of this celebration are theological after he has criticized what they celebrate”
No one, I repeat no one has ever criticized nor denied the fact of the birth of Christ. but rather the celebration invented. And this is what was pointed out. As for the fact of his birth this is practically an article of faith in all three religions. The only difference in the matter is who is the messiah. Thus, all aspects of the birth of the messiah are real and theological.
“If any western Muslim read this article they will notice its errors”
Then Only a western Muslim should make this comment. Because only westerns have translated it.
 Habib Mashhoor Al ‘Adani
3 For the customs of the people are vain: for one cutteth a tree out of the forest, the work of the hands of the workman, with the axe.
4 They deck it with silver and with gold; they fasten it with nails and with hammers, that it move not.
5 They are upright as the palm tree, but speak not: they must needs be borne, because they cannot go. Be not afraid of them; for they cannot do evil, neither also is it in them to do good.
 John Wenham, Redating Matthew, Mark, and Luke, (London: Hodder and Stoughton, 1991) p116.
 Duling 2010, p. 298-299.
 Please see: Magi, Men or Kings Pick one. https://muhibaddeen.com/2014/06/10/magi-men-or-kings-pick-one