Accidental Aesop: "If you harass someone enough, they'll eventually do what you want them to do just to get you to leave them alone!"
Accidental Innuendo: "Could you, would you, with a goat?", "I would not, could not, with a goat!"
The animated short is popular for Youtube Poop for this very reason.
"In the dark? Here in the dark? Would you, could you, in the dark?", "I would not, could not in the dark!"
Alternative Character Interpretation: Is the Guy-Who-Is-Not-Sam-I-Am reluctant to eat the titular dish based on its appearance/color alone, or is his refusal based on his self-proclaimed dislike of Sam-I-Am and the subsequent desire to not give Sam the satisfaction of having got him to do something?
Is Sam-I-Am just someone who wants to share food? Or is he a stalker who won't relent until he gets his way? Is he persistent? Or is he an example of how not to market products?
Designated Hero: Sam-I-Am stalks, harasses, and even kidnaps the nameless character because he won't try green eggs and ham. He's vindicated by the end because the nameless character ended up liking them.
Fan Nickname: Sam-I'm-Not for the nameless character Sam-I-Am keeps pestering.
Ho Yay: It's possible to see the book as having a gay subtext. Sam-I-Am is offering something at once familiar and yet with an initially-unappealing aspect to it to Sam-I'm-Not ... like same-sex relations. He is convinced that Sam-I'm-Not really, really, deep down inside likes it and he knows this. Sam-I'm-Not resists this doggedly, which has to make Sam-I-Am even more convinced that he understands Sam-I'm-Not better than he himself does.
The Living Books adaptation becomes especially suspect to this by the end, with Sam-I'm-Not preparing and feeding Sam-I-Am a giant (blue) roast turkey and eventually leading up to them both walking arm-in-arm into the sunset.