Is it considered a divorce if the husband says to his wife: "I will never divorce you for such a small problem as this, and even people, when they learn that I divorced because of this problem, will be astonished by the reason for the divorce, so I will not divorce you," with his intention being that if he were to divorce her, people would know?

The husband's statement to his wife, "I will never divorce you for such a small problem," is not a divorce and has no legal implications. Divorce is inherently disliked, and a woman is forbidden from seeking a divorce without a valid reason, as the Prophet (peace be upon him) said: "Any woman who asks her husband for divorce without a sound reason, the scent of Paradise will be forbidden to her." It is incumbent upon both spouses to live together amicably, with understanding, compassion, and overlooking minor faults.