This reminds me of a button I saw recently.
We are not with you.
We are not terrorists.
We are not alone.
Canada did not support the attack on Iraq, for very good reasons. We are a staunch ally of the US, on a national and personal level. But we are now in the position of a teen ager whose best friend wants to date a girl who is no good for him. We know it, France, Germany, and most of Great Britain knows it, but he's going to do it anyway. All we can do is hope it works out.
At the Nuremburg trials a category of 'crime against peace' was defined, some Nazis were I think, hanged for it. Invading another country to overthrow its government (even if you REALLY REALLY believe they're holding WMDs), just may be such a crime (even if you call it regime change). And it sure is a bad example for places like India and Pakistan, who've got the bomb.
So no, we don't support you , and we will speak against your actions, but to say that means we should fight on the other side is an example of the fallacy of the excluded middle. And a fallacious argument isn't wrong, it's just falllacious.