Pakistan, Oct. 4 -- For much of the 20th century, Israel and Turkey were among the Middle East's most significant strategic partners. Their militaries trained together, Israeli defence technology flowed into Turkey, and trade and intelligence cooperation helped bind the relationship together. Both countries saw value in containing regional instability, and their partnership offered a rare bridge between Israel and a major Muslim power. That world has disappeared.

The deterioration in Israeli-Turkish relations is often attributed to the Gaza war. However, Gaza is only the most visible expression of a deeper strategic realignment. Beneath the rhetoric lies a more consequential question: what kind of Middle East do Israel and Turkey want to...