Scarecrow, Tin Man, and Cowardly Lion aren’t really individuals with Enneagram numbers, they’re archetypes. Head Type, respectively, Heart, and Body.
If I were trying to describe the general idea of the personality Enneagram to children, what better reference to use than the Oz books?
Scarecrow is torn apart by the flying monkeys. His body is destroyed. A Head Type will value reason and ideas over physical capability. He’s not heartless — he loves Dorothy — but the heart for a Head Type is more a biological part rather than an emotional center.
TIn Man is strong and probably the best fighter (until Lion finds his peace), yet he hardly credits it. Emotion, love, feelings are what matters most to a Heart Type. When he can’t feel, because his heart is missing, he is incomplete and in turmoil.
Cowardly Lion is hyper-emotional. Fear drives him. He’s unbelievably strong, yet feelings keep him from remembering that. It’s only when no other companion has the capability — in the book Lion must jump them across a ravine, iirc — that he taps into his power. A Body Type is disoriented if they can’t (or don’t) use their physicality.
Each one believes he can’t do the one thing he’s good at.
The joke is that Scarecrow, who says he’s brainless, is actually smart. Tin Man is emotional and Lion is physical, despite their objections. It’s not as clear in the movie as it is in the book, but each does something that refutes their claim to failure. And the Wizard, knowing that each possesses his desired trait already, gives them some bogus gift that acts as a placebo.
It’s a good little lesson about having faith and trust in yourself.