Inertia subgroup of a p-adic Lie group is infinite

Question

It is stated here (very end of the 3rd page) that the inertia subgroup of the p-adic Lie group ${\rm Gal}(K_{\infty}/K)$ is infinite when the dimension of ${\rm Gal}(K_{\infty}/K)$ is greater than $2$ (here $K$ is a finite extension of $\mathbf{Q}_p$, $K\subset K_{\infty}\subset\overline{\mathbf{Q}_p}$ and $K_{\infty}/K$ is Galois). It is stated as obvious but I don't get why it is true. Any help is appreciated.