At that moment in the story's conclusion, Nick does feel certain that he will never die. The psychology of his feelings is no doubt complex. First of all, Nick is young. The young generally view death as the companion of old age, and when one is young, growing old is something that happens to others. Furthermore, the passing of time is experienced differently by the young. In a young life, two days can seem an eternity; the passing of sixty, seventy, or eighty years is incomprehensible.
However, inside the shanty after his father had delivered the baby, Nick saw a different face of death; he saw the blood and the horror of a man's having cut his own throat. Once outside and back in the boat on the lake, the very real sight of that leaves Nick's mind quickly as his familiar world surrounds him:
The sun was coming up over the hills. A bass jumped, making a circle in the water. Nick trailed his hand in the water. It felt warm in the sharp chill of the morning.
It is at this point in the story, "[i]n the early morning on the lake sitting in the stern of the boat with his father rowing," that Nick disassociates himself with death. Death, as he has just seen it, has nothing to do with his world--and therefore, nothing to do with himself.
Nick believes it, but on a deeper psychological level, perhaps he believes it because he must believe it. Considering the horror and the brutality he has just experienced, psychological denial would explain his certainty. In another Nick Adams story, "Big, Two-Hearted River," Nick appears as a young man returning home from the war, working hard to repress memories of that which he cannot endure to relive, another form of denial and a Hemingway motif.