The word "classic" is usually flung at any TV show that predates 1975 television history just isn't that long. "A Charlie Brown Christmas", however, earns the label.
Truly classic art changes our view of its subject. "Charlie Brown" is the rare show that takes children's humanity and spirituality seriously. Compare it to contemporary shows featuring kids, usually presented as well-groomed, slow-witted props needing adult guidance at every step. Comparatively, Charlie's heartbreaking compassion, Linus' uncomplicated faith, and Lucy's shallow but joyful embrace of materialism are all presented without condescension.
The show lacks the technical whiz-bang of great animation really, it would work just as well as a radio play (Vince Guaraldi's funky, sparkling jazz score is great listening). But the show's visual simplicity matches the hip modernism popular in the early 60's and the comic strip's format (note how so much of the action scrolls left-to-right-to-left, just like a horizontal strip).
Who hasn't go-go danced along with the Xmas pageant kids? Who didn't yearn to play "Linus and Lucy" at a piano recital? Who hasn't lit up inside when Charlie's tree is transformed? Watch it. It's a classic.