In Turkish propaganda, any form of Kurds organizing themselves, be it inside Turkey our outside in Iran, Iraq or Syria, is "terrorism". Even though most of this activity is political and from a democratic standpoint quite "legitimate". Even much of what the PKK has been doing historically falls under that umbrella.
Also the Kurds are forming a state in parts of Syria and Iraq, where the "original" state is not able to restore order, especially against islamic militants. On top of that, the Turkish security forces have a long history of prosecuting Kurdish civilians. This makes the whole label of "terrorism" extremely murky and what Erdogan wants of NATO is much less nice than support against terrorists: He wants support and acquiescence in his war against Kurdish forces, including outside Turkey.