Not sure how effective this image is at getting this idea across, so here is an overexplanation of what is going on here:
- In most clip show episodes that Woolsey is featured in (and really most of his episodes of Stargate SG-1 in general), his character is an antagonist. His goal is usually to shut down the SGC, or something like that.
- By the final clip show episode, Woolsey is actually now the leader of the Atlantis expedition, which is (in some ways) an extension of the SGC. In that episode, Woolsey is now defending the existence of the Atlantis expedition, and by extension, the interests of the SGC.
- This is similar to the role that the titular character plays in the first two Terminator films. In the first, the Terminator is clearly the antagonist, whose goal is to kill the protagonist. In the second film, that same Terminator is now actually a protagonist, whose goal is to protect the other protagonists.
I didn't ever see him as an antagonist, that was more Kinsey(?)
He is a bureaucrat doing a job to the best of his ability. He knew from the start he was brought in by the wrong side and when he does the alpha site tour that ends in disaster, he knows he picked the right side. Which is likely why he got picked to replace Sam.