The story
Blend of Mithras + Christmas. In reference to one Roman Dies Natalis Solis Invicti associated with December 25 and unrelated to Mithraism. Sol Invictus was also conflated with or used as an epithet of Mithras, from where the confused misidentification arose. Apparently coined by Gwendolyn MacEwen.
Etymology from Wiktionary, CC BY-SA 4.0.