The thing is, NATO does not support the Kurds and is at best neutral with the YPG. It will side with Turkey in a heartbeat in any conflict.

President Obama had even promised that he would assist so that Kurds were no longer east of the Euphrates.

https://www.washingtonpost.com/world/biden-visits-turkey-on-mission-to-repair-strained-relations/2016/08/24/bc684904-6a04-11e6-99bf-f0cf3a6449a6_story.html?utm_term=.95dab3f46bdd