"GWB gave those reasons before the war started. It was found to be false after the fall of Baghdad"

Yes G, but you are (deliberately I suspect) missing the point.

Let's add to the timeline:
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GWB gave reasons

Baghdad fell

trailers found

intelligence determines they are not WMD-related

intelligence informs Whitehouse

Bush says they are WMD-related
Bush, Cheyney et. al. continue to claim they are WMD-related for over a year.
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See how the abbreviated account in your post conveniently stops before the lie begins?