Throughout much of the story, the reader has to use inference, or educated guessing through the use of context clues, to figure out exactly why John's tribe behaves in the many ways that it does. To us, people who never touch any piece of metal might seem strange and overly superstitious. However, if you read carefully, you can look at the following clues, and start to piece together an idea of why his tribe has developed this practice. The first clue is that John refers to "the great burning" that destroyed most people on the planet. If you think about that, it would have to be a very, very large event to wipe out most people. Possibilities? Meteor hitting earth, or a nuclear bomb. If it was nuclear bomb, there would be a lot of leftover radiation. Next clue: John refers to Dead Places, where everything is dead, including the people that lived there. If you combine that clue with place that they aren't allowed to go, namely a City, then you can hone in more closely on the nuclear bomb scenario--bombs are normally dropped on cities, and wipe out the city and everything surrounding them for a while. That would make everything in its radius "dead".
So, piecing together those clues, and assuming that it was a nuclear bomb that took out the cities and killed everyone, then you can assume that the metal products contained radiation levels for a very, very long time. Imagine the first survivors foraging for supplies and handling the metal; they would have gotten sick from radiation poisoning and died. The people would have passed that knowledge down from generation to generation, and eventually, it would become one of their rules. The reason why might be lost, but the rule is still followed. I hope that those thoughts help a bit; good luck!