The claim is that bronze enabled complex, highly centralized states because it was rare (due to a dearth of tin). So only the connected/rich could afford it, and they used it to build empires/kingdoms/etc.

Iron wasn't superior to bronze (in the fact the article claims it was worse), but it was good enough and widespread. All you needed was a furnace with bellows, charcoal, and an iron source (which were everywhere). Since everyone had access to iron, no one person/group had an edge over the others and this prevented highly centralized polities from being established.