The answer, of course, is that they didn't: the question of disarmament and diplomatic initiatives was not undertaken for the purpose of preventing the war, but for the purpose of further authorizing it. The war itself had well understood other grounds for its waging, as well as a Congressional Resolution in 1998 which set American policy. Once Saddam showed that being defeated did not mean that he was going to comply with the cease-fire in place, is it all that surprising that the United States following its own rules, and policies in place, got set to take him out? When there had been various moves on his part to deploy WMDs against his own population, is it surprising that we would consider that as a minor factor in our own calculations?
That we weren't listening to the UN seriously is because whenever we do, we regret it.