That's because the Kurds want an independent Kurdistan to extend far beyond Syria's borders. The Kurds live in and would claim parts of not only Syria, but also Iraq, Turkey, and Iran, from the Mediterranean to the Caspian Sea.
That's a lot of governments losing land, and a lot of oil changing ownership. It's also another sect of Islam vying with the others for supremacy in the ME. The current rulers will not be in favor of that.
In Syria that is not the case, the majority of Syrian Kurds are not Muslim. Significant percentages of Atheists, Christian (Assyrian & converts). The Kurds who are Muslim are almost totally sectarian in outlook. In Iraq they are very high percentage Muslim (roughly 75/25 Sunni/Shia)