Granger describes the mythological phoenix which, every few hundred years, would burn itself up, and be reborn from its ashes. Granger adds that the society of humans does the same thing. The only difference is that humans knowingly destroy themselves in a similar cycle; this is what makes it all the more frustrating. The phoenix dies and rises again because that is its nature. Humans do the same (destroy each other and rise again) even though they are aware they are destroying themselves.
Granger's plan is for he and his fellow book people to keep reading and remembering. Then, they will pass their knowledge onto the next generation who will repeat the process. According to Granger, the most important thing is to give something to the world, to change the world in some way, large or small. Passing on knowledge is one way to do this. He believes that someday the knowledge they carry will help someone. And his great hope is that someday people will finally wise up enough to stop the silly cycle of destruction and beginning all over again. Granger says to Montag:
And when they ask us what we're doing, you can say, We're remembering. That's where we'll win out in the long run. And some day we'll remember so much that we'll build the biggest steamshovel in history and dig the biggest grave of all time and shove war in and cover it up.
Granger compares his society to the phoenix, a "silly damn bird" which is consumed by fire but then rises up from the ashes. The important point to note here is that the phoenix does this time after time. It never learns from its mistake.
For Granger, society is like the phoenix because it, too, never learns from it mistakes. Quite literally, his society allows itself to be engulfed in flames—the flames of the firemen—as it seeks to destroy books and book-reading. Just like the phoenix, it does not realize that these flames are the problem. If society did not censor reading and set fire to books, it would not have to go through this destructive process.
Granger, therefore, believes that society must learn from this mistake if is it going to change for the better. It must learn from the past, it must embrace books and reading, and, more importantly, it must get rid of the firemen's flames. If not, society will continue to destroy itself, just like the phoenix.