This is just the old tussle over land, Turkey vs Syria, with the mobile element of the Kurds from both sides of the porous borders making up the triangle. The Kurds can and do play both sides.
Neither Sunni Turkey nor Alawite/Shia Syria want the Kurds to declare their own nation.
Turkey and the Syrian SDF rebels now happen to be allied and advancing south against the Afrin Kurds, who will accept help from anyone, even the Syrian government or supporters of. Syria would not like Turkey to succeed on Syrian lands, naturally. Syria is backed by Russia, Iran and Hezbollah.
The Syrian FSA is backed by the US, and allied with Kurds east of the Euphrates. The US is playing a waiting game, but many of their sympathies probably still lie more with Sunni Turkey, and not with the Syrian Assad regime.
There we are, clear as mud.