First off, as many leaders of what they themselves refer to as organizations to throw off the yoke of american imperialism, and what the rest of us call terrorist organizations, say, W has been great for recruitment.
Their cause for war is the claim that the United States and Israel seek to wipe out Islam and steal the natural resources with which the Middle East is cursed.
No US president has come anywhere near W in terms of making this claim seem valid, both in its religious and economic parts.
you can argue that W.'s invasion of Iraq was not guided by Christian apocalypticism or corporate greed, and you may be right, but that's not how it's being perceived.
So, whatever else you might say, W. is better at encouraging terrorist groups to recruit and to organize against the US.
Personally, I don't see kicking his dumb bellybutton out of office as "backing down" or "giving in" to the wishes of terrorists. Frankly, Al-Q and the rest want someone like Bush in power. It makes their extremist position seem not so extreme.
And if you've got a quarrel with a neighbor who's convinced you want to damage his property, you don't apologize for something you don't want and don't desire to do, but you don't let your kids throw rocks through his windows either. It's not "backing down" to tell that kid to stop and lock him in the basement for crimes against humanity. There's a right way and a wrong way to solve problems, after all.