The Mugen train hurt him physically and emotionally. His pride was being a Flame Hashira and not disappointing his father. Kyōjurō saw death before his eyes. He couldn't go on, losing an eye, being on the brink of death... He didn't want to experience that again.
Furthermore, his wife was waiting for him at home, always waiting for him; he didn't want to leave her life and the child growing in her womb.
You cradled the little baby as you sat on the engawa in the Kyōjuro mansion, stroking the baby's little nose.
Kyōjurō: “You take such good care of our son.”
Rengoku said soothingly, sitting down next to you, crossing his arms and looking at the baby in his wife's lap.
Kyōjurō: “I wish he had your hair... But what can I do? All Kyōjurōs look alike. Copying each other in appearance. We still have to decide on our son's name.”