It's incorrect to assume that just because Gundam states that both sides have problems that makes them morally equivalent. I mean it is the case in some series, but 0079? No.
And Zeon could just have... not started the war. The war happens when Zeon wants it, because Zeon started the war.
Also I'm hesitant to accept the logic that the garrisons were a major threat when most recountings of the opening month of the war go "and then the EFSF got their shut pushed by Zakus, like every ship they had died, it was a massacre you guys."
The slaughter of the spacenoids was not done because of ideology, no, but it was done merely because it happened to be slightly convenient to Zeon at the time to massacre countless innocents for geopolitical gains in a war they started.