Why people believed Saddam had nukes

It's pretty common knowledge. If he let on that he didn't have them, he probably would of been overthrown withing a few years by people in his own country; either those loyal to Iran (more then likely) or ones wanting just to get rid of him so they can take the reigns of power (lesser chance of success.) Iran was the most direct threat to Saddam, and it may of been easier to fabricate information to say he had begun to stockpile it again then it would of been to actually start producing them. Considering he had no problem using them against Iran in the Iran-Iraq war, and used them again against his own people when they rebelled shows he already had the know how on how to make them and the will to use them. And most toxic agents can be easily made with simple everyday chemicals and doesn't need all that much space to produce a decent amount (mostly for storage till you can move the finished bomb, shell, mortar, or pressure tanks holding it.)

The media seems to have it in their head that you need large facilities to manufacture chemical weapons due to the sizes the US, Russia, Britain, and other countries that used to produce it until either eliminating them from their arsenal or reducing their stockpiles to the bare minimum. If you have refineries in your country, and the ability to produce a container to hold the agent, then any country has the possibility of being able to produce chemical agents. It wouldn't be hard to let false information slip to your enemies saying you have the ability to produce and are producing, it sure beats some alternatives. I'm willing to bet he miscalculated on the US's response (with more fears of worse case scenarios brought on by 9-11 in the US government and its intelligence agencies) and was playing towards keeping Iran uncertain of his response to an attack or attempted overthrow.