The answer to this can be found towards the end of Chapter 12. Specifically, it can be found on p. 236 of the paperback edition of the book. There, Diamond tells us that hunter-gatherers never invented writing on their own and never even borrowed it from others
…because they lacked both the institutional uses of early writing and the social and agricultural mechanisms for generating the food surpluses required to feed scribes.
There are two aspects to this argument.
First, there is the idea that food surpluses are needed. Earlier in the chapter, Diamond tells us that early writing systems were devised by a small group of scribes and were only used by those people. What this means is that there had to be some people who had the leisure to sit around inventing ways to write and then doing actual writing. Those people could only exist if someone else was getting food for them because they were not working to get their own food. Hunter-gatherers cannot typically get that much food and everyone has to work in getting food. This means that such societies couldn’t have scribes.
Second, there is the idea that hunter-gatherers had no use for writing. This is because, Diamond says, writing was used mainly for record-keeping. It was used to keep track of who had how much wealth and, therefore, how much they owed in taxes. Hunter-gatherer societies do not have accumulated wealth and they do not have systems of taxation. Therefore, they would not have had any use for the early forms of writing.
For these reasons, hunter-gatherers did not have writing and civilizations did.