No, support for a war is anything that prolongs the war, no matter which side you're arming.

You're essentially saying "it's not support for the war if I'm (perceiving I am) making sure my team wins". I'm not faulting you for that, it's the most common position, but it is support for war.

If you want to define exercise of the right of collective self-defense against aggression as “support for war”, fine, you can have your own private language.

But now explain why that, in the face of actual aggression and genocide, is a bad thing compared to the alternative?

He's not talking about the right of the "infringed" collective to self-defense. He's saying, I think, that when you as a 3rd party enter the conflict you are adding flame to the fire. edit: noting that I'm not trying to be pro/con a third party entering the conflict. I'm just trying to be guiltless action.

I think you're waving at a sign saying "some things are worth war" and maybe that's true but for most things that's "support for war".

In this case there's a more important point, though, that a broad understanding that war will not be allowed to change the status quo will decrease the number of wars. Building and maintaining that understanding has the expense (sometimes) of making individual wars longer, but when it is (at worst) unclear which of those effects dominates it is unreasonable to label picking one side of that trade as unequivocal "support for war".