This. And, even if not aimed “properly”, a gun in the mouth will almost certainly ping the brain stem, or a good part of it. Since the brain stem is densely packed with various connections and control centres, any injury to it is life-threatening.
For those not too familiar with neuroanatomy, the brainstem is the densely packed, compact part of the brain through which every connection to and from the brain travels, and in which are located centres for control of breathing and other basic life functions.
It is also worth mentioning that consciousness resides in the brain stem, or at least depends on an intact brain stem. In other words, you will be unconscious the instant the brain stem is hit (either directly by the bullet or a bone fragment, or torn apart by the tremendous shock and pressure waves generated by the gunshot).