Why can't we define any $C^{\infty}$ structure on the single point $0 \in \Bbb R^n$?

Question

I'm studying the book "Differentiable Manifolds" by Brickell &Clark . On page 94, in the example 6.3.6, it was written that we can't define any $C^{\infty}$ structure on the single point $0$. Isn't the single point $0$ a $C^{\infty}$ manifold of dimension 0?

Thank you for your any help.