Why is being divergent dangerous?
Similarly one may ask, what does it mean if you are divergent?
Divergence is the tendency to diverge from the norm which is, in this case, the mindset and way of thinking the factions are meant for. If you get a faction choice of more than one from the results of your aptitude test, you are considered Divergent.
Similarly, what is the main problem in divergent?
The main issue in Divergent, similar to most Dystopian novels, is a faulty society/government. In Divergent, they attempt to fix this by instituting a Faction system, each faction blaming a different reason for the governments failure. Their are five factions, Dauntless, Amity, Candor, Erudite, and Abnegation.
The city has had numerous failed attempts in which the GPs (Divergent) were being slaughtered and outbreaks of war ( hence the damaged roads and buildings. The wall is meant to keep the inhabitants from leaving the city therefore disrupting the tests.