The closest Hemingway comes to answering this question directly in the story is Nick's father's reply when Nick asks him why the man killed himself: "I don't know, Nick. He couldn't stand things, I guess." What the husband "couldn't stand" can be found in the facts of the story and the inferences we can draw from them.
When Nick, his father (the doctor), and Nick's Uncle George enter the shanty at the Indian camp, the young woman had labored for two days to deliver her baby (a breech birth) and her husband lay on the bunk above hers, having hurt his foot with an axe three days before. She has suffered and screamed in pain; for two days, her husband has lain above her, listening to her cries--unable to help and unable to escape the sounds of her suffering, unlike almost all the other men in camp who have gone up the road so that they do not have to hear her.
After examining his patient, Nick's father performs a Caesarian section to take the baby that cannot be delivered naturally. This, a major operation, is endured without anesthesia by the young woman as four men hold her down. The doctor operates with a jack-knife and sews up the incision with his fishing gear. Her agony can only be imagined, for Hemingway notes it not at all, except to say that she bit Uncle George as she was being held down before the surgery actually began.
As the horror took place below him, the husband lay above, listening. Nick's father had given no thought to his feelings as he experienced his wife's agony, just as Nick's father considered his patient's screams (and the suffering they expressed) unimportant. The doctor had explained nothing to him nor given him any reassurance as to the outcome of his wife's ordeal. Neither he nor his wife had been prepared in any way for what would take place. In his horror and helplessness, the young husband cuts his own throat, his only escape from the unbearable situation. He died before his son was born. He couldn't "stand things" any longer.