It probably comes from theatre. If you watch J-dramas, you'll notice the acting tends to come off as "anime-ish", and it would only make sense to use a "gesture language" like that on stage, so audiences can see clearly what an actor's feelings are.
You'd probably have more success comparing anime to opera or musicals than to western film and television.
You'd probably have more success comparing anime to opera or musicals than to western film and television.