In Insurgent, the factions are kind of like sports teams. People wear the colors of whomever they're aligned with, and they act as though their faction (or favorite team) can do no wrong. Almost all the factions think of themselves as the New England Patriots, even the ones who are actually more like the Arizona Cardinals.
Loyalty is a big deal within the factions. People are expected to act as their faction expects them to act and never deviate. This becomes quite a problem with Tris, who is Divergent and can be a part of any faction. She can't even decide whether to be loyal to her boyfriend or to her boyfriend's father, the two of whom have opposing ideas on what's best for the city. Perhaps the only person Tris can be loyal to is herself?
Questions About Loyalty
Why are some people loyal to their factions and some people not? Do the factionless have any loyalty?
Why is being disloyal practically a crime worse than murder in this society?
Who is Tris loyal to? Does she tend to be disloyal because of her Divergence?
Why does Caleb choose to pledge his loyalty to Jeanine instead of Tris?
Chew on This
Putting such a high value on loyalty makes the people more divided, because people stay within their factions instead of associating with anyone else.
Loyalty that is dictated by laws or rules isn't real loyalty. Only actions and choices made freely can be considered truly loyal.