Cybermen, especially the Mark VII onwards, are almost always humans that have been converted into Cybermen. They enhance their logic and suppress their emotions through this process, however, time and again they've proven that within the metal shells, they are still human.
For instance, Danny Pink, an ex-soldier who was converted into a Cyberman after he died in a car accident, still had feelings for his girlfriend, Clara Oswald, due to his emotion suppressor failing to activate. And even after his emotions were suppressed, he still had enough of a sense of self to help the Doctor command an entire army of Cybermen to self-destruct.
They are, in essence, robots. But, their souls are still preserved, doubly so on the fact that Missy, the latest reincarnation of the Master, was literally keeping souls in "heaven" so she could later transfer them to her Cyberman army.