Distance vector protocols work by "routing by rumor." Each router only knows what its neighbors tell it.
Here's the process:
Router A tells Router B: "I can reach network X with cost "
Router B adds its cost to A (say ) and records: "I can reach X via A with cost "
Router B tells its neighbors: "I can reach X with cost "
The problem: if A's path to X fails, B might hear about an alternate path through C that actually goes back through A. This creates a routing loop. Distance vector protocols need mechanisms like split horizon and poison reverse to prevent loops.