Gah, Sirin can't decide which bandwagon she wants to jump on, mostly because she's not very good at expressing her reasonings.
(which is to say that I'M not very good at expressing it...)
The way that Berserker and Melkor are going seems more appealing to her, simply because she feels that non-combatants and the potential free minds shouldn't have to pay for a war they don't even know about.
As Ush mentioned, there IS a difference between killing the SWAT and policemen that chase after us than all the billions of civilians in the Matrix. Civilian casualties always happen in war, but billions of civilian casualties? That's insane!
And pro-Virus actually really does sound exactly like Sennacherib. He believed that Humanity should have been ended, executed, exterminated. As long as a few Machines survived, it was victory. That could be said of Zion, if we exterminated the Matrix in this way. It's too much like Sennacherib for Sirin to be comfortable agreeing with it.