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Correct me if I'm wrong but aren't we backing the SAA?
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No.
SAA is the Syrian Arab Army,the government forces.A large portion of those fighting for Assad are now Iranians, Lebanese Hezbollah,Iraqi Kataib Hezbollah,Palestinian Liwa al Quds and Hazara mercenaries from Afghanistan.
The Free Syria Army is an umbrella for all non-jihadist opposition to Assad. The US primarily supports the Syrian Democratic Forces portion of the FSA which is comprised of anti-Assad Sunni Arabs,Assyrian Christians and Kurds of the PYD.
Turkey opposes the SAA and supports a portion of the FSA that is in conflict with the SDF. Turkey is now fighting both the regime and the elements the US supports. It also occasionally fights and colludes with the Islamic State.
Qatar and to a less overt extent KSA and Jordan support jihadi groups not part of the FSA that are primarily fighting Assad but also FSA/SDF.
Clear as mud?