In the movie In the Loop, a government minister accidentally said something ambiguous about a war.
How did this actually result in a war and why?
The movie is a satire about the start of the second gulf war between the western allies (including the USA & UK) and Iraq.
The plot of the movie involves different groups of people who are basically for or against the possibility of going to war against the unnamed country, primarily:
The "Doves" against war are:
The "Hawks" for a war:
The story surrounds Simon Foster (a minor UK government minister) and his assistants. Simon is a career politician and wants to both "do the right thing" but also protect his career and rise in the ranks of the UK government. He is scared of Malcolm, a character spoofing real life UK Prime Minister Tony Blair's communications director Alastair Campbell. Campbell had huge power in the UK government at the time of the beginning of the Iraq war.
So the story that is told is of Simon and his assistant bumbling around, misspeaking in interviews, and accidentally releasing (leaking) documents on behalf of the "dove" group. He tries in vain to sit on the fence and keep both the 'hawk' and 'dove' groups happy with him.
In the end the "hawk" group are forced to release a heavily doctored "dossier" of evidence to support the war - an echo of the documents released with evidence of WMDs in Iraq. The movie ends on the assumption that the war is now imminent.
So this isn't claiming this is what happened in 2003 - but it is a dramatic and comedic spoof of the sort of trail of events that could happen in such a situation. So it wasn't just about the single "war is inconceivable" comment - it was about how both sides tried to use Simon to further their side of the argument for or against war. Simon doesn't seem to want war himself, but he's too afraid to properly support the Dove's and ends up keeping neither group happy.
For more information on the background of the events it is spoofing, see the Wikipedia article on the preparations for and opposition to the invasion of Iraq. The article on Alastair Campbell's involvement in the run up to the war is also interesting.