What is the authenticity of the hadith: "May Allah curse every man who is a 'taste-tester' (frequently marries and divorces) and a 'divorcer' (frequently divorces his wives)," and does the stern warning to women against seeking divorce without reason contradict the fact that a man divorcing is merely considered reprehensible (makruh)?

The narration regarding the reprehensibility of divorce without need is a weak hadith.

As for a man divorcing his wife without need: some scholars view it as disliked (makruh), while others view it as forbidden (haram) because it causes harm without any benefit.

As for a woman seeking divorce or annulment (khul') without a valid reason: some scholars view it as disliked (makruh), while others view it as forbidden (haram).

The husband's guardianship over the wife places the power of divorce in his hand.