The Kitaev spin-S models on a honeycomb lattice are the theoretical basis for the search of exotic quantum matter in many materials, but only for S=1/2 there is an exact solution, while no analytic solution is known if S>1/2. In this talk, I will discuss the symmetries of the Kitaev spin-S model and their profound implications. In particular, I will highlight the importance of a 1-form symmetry, and the interplay between this 1-form symmetry and the ordinary 0-form symmetry. By examining these symmetries closely, we conclude that for any half-odd-integer S there must be deconfined fermionic excitations carrying no fractional quantum number under the ordinary symmetry of the Kitaev model. This conclusion is robust even if the Kitaev model is perturbed, as long as the perturbations are local and respect the symmetries. If the local perturbations are weak, this conclusion still holds even if these perturbations break the 1-form symmetry.