Ubiquitin: Good question. Not ever giving gifts doesn’t make sense, nor does on any Yom Tov, because it’s unlikely to be a copy of the goyish “minhag”. Giving on Chanukah would be the problem, since Chanukah gifts are seemingly a copy of their ???. I could definitely see a tayna that it’s only assur on Dec. 25; in fact, I wonder if even the mattirim would agree to asser then.
Jewish Thinker: If there’s religious significance, being logical doesn’t help. Google “origins of christmas gifts” to see what the significance is.