'Divide and rule' - along ethnic lines, religious lines, sex lines, etc. - is THE cornerstone of the Jews' subversive SOP to gain & wield power over others. Look for fault lines within rival nations (whether they're the host of the Jew or an external enemy) and stoke the embers within those fault lines into a raging inferno which will keep said rival nation too busy with internal conflict to pay attention to the Jews. If they could get their preferred pawns into a strong position, from where they can continue to cause trouble for the rival entity indefinitely and be a real pain in the ass to purge even before dealing with the Jews (as with blacks in post-WW2 America, and with a hypothetical Kurdistan in the Mideast) then so much the better.

In the Middle East, the Kurds have long been a militant minority without their own country who have agitated for their own independent 'Kurdistan', an aspiration which puts them in direct conflict with the countries that that Kurdistan would have to be carved out of: Turkey, Syria, Iraq and Iran. All of these except Turkey (sort of, but not really, and that's changing nowadays anyway as that country becomes increasingly Islamist) are/were Israel's regional rivals. Thus Kurds are the most convenient wedge lying around for the Jews to wield, well-positioned to cause trouble for pretty much all of their regional enemies at the same time (and already doing it even before Israel existed, at that).

On another note, the Kurds were also very heavily involved in the Armenian & Assyrian Genocides, with a lot of the footsoldiers directly doing the genociding being Kurds. As Israel is very friendly with Azerbaijan, the mountain Turks attempting to continue the bloody work of Enver Pasha to this very day, why would they not also be friendly to the descendants of the original genocidaires...