A stomach wound results in a most painful death. A person who is shot in the head stands a good chance of dying instantly and with little pain, but one who is shot in the stomach lingers in terrible agony for a long time before finally dying. Curley shows his vindictive nature in recommending that Lennie be shot in the stomach. He is angry and vengeful not only because his wife has been killed, but also because Lennie had gotten the better of him previously, in the confrontation in which his hand was broken. Curley had been humiliated and was seething with rage at Lennie already, and now that Lennie has unwittingly killed his wife, Curely wants him to suffer in revenge for what he has done.
Curley, who is an especially cruel man, seeks revenge not only for the death of his wife but more importantly for his shattered hand. Shooting Lennie "in the guts" would cause a very painful, prolonged death full of the suffering that Curley wants Lennie to experience because Curley himself suffered not only pain but also humiliation when his hand was crushed.
George must choose to kill his friend himself to spare Lennie that kind of awful, agonizing death. A bullet in the back of the head guarantees quick death; shooting him in the stomach would not.
Because it is especially cruel and painful. Curley doesn't care about his wife. He just wants to watch someone in pain. I believe that Curley is also treating Lennie like an animal by demeaning him even in death.
because if they shoot him there, it will get his organs