By definition, an insurgent rebellion fights against its own government.
Whenever the government fights such an insurgency, it's killing its own people. That's what Civil War is. If one faction of society declares all-out war on the other factions, including the central government, I don't know what kind of response you would expect. These aren't peaceful protestors who are dancing around with flowers and such.
Those terrorist assholes in Jund-al-aqsa just cut the gov't supply route to Aleppo.
http://news.yahoo.com/jihadists-cut-regime-supply-route-syrias-aleppo-monitor-111554629.html
Nobody cares, of course, and these guys in Jund al-aqsa are foreign terrorists (not Islamic State, rather part of the 'moderate Sunni rebels') but a million crocodile tears will fall if the gov't in turn cuts the Turks' supply route to their combatants in Aleppo. That Al-Qaeda is fighting the regime, nobody cares, we're actively asked to support them.
There aren't many people who affirmatively like Assad, but there are many people who point out that the 'moderate opposition' is full of little but rabid Sunni jihadis, while the parts of Syria that are actually filled with diverse, non-rabid populations are all siding with the regime. It doesn't take much brainpower to see that making the one side (the worse side) bigger and the other side (the better side) smaller = badder. Asking us to believe that the worse side will suddenly *stop* being maniacal Sunni jihadis, if only they are allowed to win, beggars belief. If it didn't work 943743209 times before, it's not going to work this time either.