In the real world, you usually hear the word "insurgent" attached to some kind of terrorist group. But in Veronica Roth's Insurgent the insurgent is actually our protagonist, Tris.
The word "insurgent" is defined for us in chapter 41: "'Insurgent,' [Fernando] says. 'Noun. A person who acts in opposition to the established authority, who is not necessarily regarded as a belligerent'" (41.10). Well, that describes Tris to a T. Except the belligerent part. She is definitely belligerent.
So put yourself in Jeanine's shoes. Or Marcus's. Or Eric's. Who would view Tris as an insurgent? Is she going against the government of her city? And if so, does that pretty much make her a terrorist? Is she an anti-hero? Should we be rooting for her at all? And why do all the books in this series have to end in –ent? What's next? Detergent?