<p>Now that I realize you are talking about inviting a professor and his wife to a family holiday dinner I feel differently than if you were just asking a professor to join you for dinner. The latter is 100% weird. The current situation isn’t that weird. I think rebecca’s concerns are reasonable but can be easily handled in the way the invite is extended. Acknowledge that they may not celebrate christmas or may want to celebrate christmas themselves but if they would like to, you and your family would certainly enjoy their company and would like to include them in your celebration (this is all assuming your family is ok with it, which needs to happen before you say anything to the prof).</p>
<p>My mom has friendships with several of my high school teachers on her own (one of whom actually never taught me since she taught a foreign language I didn’t take) so it’s not like it’s out of the question to invite them but it does have to be handled tactfully.</p>