The climax of "The Dead" features a breakdown in Gretta that is preceded by a near-breakdown in Gabriel. The two experience emotional turmoil for quite different reasons.
Gabriel begins to watch his wife closely as they prepare to leave the party. He sees her listening intently to a song being sung. She is the only person who recalls the name of the song. The details of the narrative, given through the character of Gabriel, suggest that Gretta has undergone a change of some kind.
Gabriel and Gretta return to their hotel, where Gabriel becomes frustrated and upset. He desires to make love to his wife - and to express his affections for her verbally - but she resists. Gabriel enters a state of agitation when this happens. His mind begins to race.
Then Gretta tells Gabriel about a young man she once knew and loved who died when he was seventeen. Gretta breaks into tears at telling the story and Gabriel finds himself internally at odds. He wishes to be vindictive but finds himself acting and speaking kindly.
He does not feel kind. The lack of control over his emotions is a central idea in the text and takes an important role in this moment, the story's climax. Gabriel is subject to his emotions, as the climax unfolds, not the other way around. This situation is something of a trap.
Earlier Gabriel thought about how nice it would be to take a walk, alone, outside in the snow. He wishes to be free and in command of himself. His inability to achieve this is finally overcome when he experiences some empathy for his wife, accepting the feelings that he cannot control.
He feels his soul has reached the place of the dead and that the living world is becoming nonexistent, as if he is outside his body.