"Rocco's a rock, Zoe! Rocco won't know the difference!" shouts Elmo.
Zoe tells him that Rocco is set on eating the sweet treat - and that's when Elmo dives into a full-on tantrum.
Elmo says: "How? How is Rocco going to eat that cookie, Zoe? Tell Elmo! Rocco doesn't even have a mouth! Rocco's just a rock! Rocco's not alive!"
The clip has been viewed more than 7.2 million times since it was posted on Twitter.
New Zealand actress Melanie Lynskey was among several who commented about the clip.
"The joy that Elmo's righteous fury over Rocco has brought me and @JasonRitter for the last three years of parenting ... Thank you Sesame Street," she posted.
Elmo himself was forced to address the controversy.
"Don't worry everybody! Elmo and Zoe practised sharing and are still best buds forever! Elmo loves you Zoe! Ha ha ha!"
Despite his statement, he did not apologise to Rocco.
"Elmo doesn't want to talk about Rocco," the official Twitter account added.
He doubled down on his opinion too: "Has anybody ever seen a rock eat a cookie? Elmo is just curious."
NBC News delved deep into the origin story of Rocco, and concluded the clip in question represents a long-standing feud between the two characters.
What might be even more shocking to parents is that Elmo's less-than-civil behaviour actually ends up winning the argument.
Gabi pointed out that Elmo is in the right because the pet rock is not actually alive, and therefore does not have feelings or an appetite.
