Why did Granger propose that a mirror factory is the first order of business in a new society?

The mirror factory must be understood as a metaphor. To be able to change the attitude of society, they need a reflection of what they have done. In contrast to the parlor walls, mirrors are made for that. They reflect the person who is looking inside as they are. The parlor walls of Fahrenheit 451 just showed the humans what they wanted to see without giving them the possibility to see the real world.By entertaining them all tht time, they make them losing the reality of life.

The unconcealed look of a mirror would be necessary for the society of Fahrenheit 451 to have a chance to change something after the war.

With self-reflection, they should be able to avoid the repetition of former society catastrophes, a system which is described by Karl Marx in his state-theory.

Granger wants to try to change this circle of history by showing the humans their mistakes, like a mirror shows a human itself.