experimental chemistry - Why isn't dry CaCl₂ used to dry HCl gas instead of concentrated sulfuric acid?

In our chemistry books, it is said that concentrated sulphuric acid is used to dry $\ce{HCl}$ gas.

But, concentrated sulphuric acid is a strong oxidising agent so, why isn't $\ce{HCl}$ gas oxidised to $\ce{H2O}$ and chlorine gas?

Why dry $\ce{CaCl2}$ (Calcium Chloride) isn't used as drying agent?

[Note: $\ce{CaCl2}$ have no reaction with $\ce{HCl}$ as they both have chloride ion in common]

Answer

Why does concentrated $\ce{H_2SO_4}$ oxidise? Due to the nascent oxygen it gives: $$\ce{H_2SO_4}\rightleftharpoons\ce{SO_2 +H_2O +[O]}$$

Now, if you want $\ce{HCl}$ to be oxidised, the following reaction must exist: $$\ce{HCl} +\ce{[O]}\rightarrow\ce{HClO}$$

But, you can observe that the reaction $$\ce{HClO}\rightarrow\ce{HCl} +\ce{[O]}$$ can't be backward under normal conditions (you probably have read this reaction in the bleaching action of bleaching powder). So, fortunately, you can safely use $\ce{H_2SO_4}$ in this purpose...and take its advantage to $\ce{CaCl_2}$, as agha rehan abbas and Molx mentioned.