There are a lot of strips about arguments and their nature right now. Schulz and Peanuts: A Biography notes that he got a lot of ideas for the strip from his social circle, including characters and pastimes, so presumably this strip about arguments originated from his observations of real arguments in his group.
It is a little-known fact that Charles Schulz started a second, short-lived comic strip later on, called It's Only A Game, the U.S. Acres to Peanuts' Garfield. My guess was he started it as an outlet for many gaming-oriented ideas sparked by his social circle that would be out of place in Peanuts.
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