Good question. It is explained in the video.

The Bush administration masterfully made out that the anthrax, which came from US Army bio-warfare labs, were an attack by Saddam Hussein's Iraq, and the media repeated those claims and amplified them.

The WTC attacks were bad enough, but they were an attack on the most privileged power centers of the US. But the anthrax attacks came in the mail and felt like it could attack anyone. Liberal journalists were being attacked. Ordinary people felt like the attacks were aimed at them, not the power centers of the nation. They went out and bought anthrax-proof masks, made safe-rooms, stocked up on anti-anthrax meds.

You can also read this that explains why liberal journalists linked the anthrax attacks with Saddam Hussein and convinced them to support the unprovoked invasion, and how quickly they memory-holed that panic.