Very good input in the other answers. I like to add a second thought, too. Afghan hounds are a very old breed. They are genetically very close to wolves which means that their genes are very old, very original dog. Approaching another dog nose to nose is very impolite. Staring at other dogs is also very impolite.
Your dog with the oldest genetics met a fairly younger dog, one of those who often (due to their breeding) stare at others in the most impolite ways (in dog speech). This situation triggered something in his very old behaviourism. Afghans are wonderful dogs but you need to understand that they are not your average neighbourhood pooch ( plus oriental sighthound breeds are always guard dogs, too).