system
Given the following post, respond as if you're commenting on Reddit:
human
[GTA V] Why do the FIB and IAA shoot each other?

During "The Wrap Up", Sanchez rats out Haines, Norton and Michael to the FIB. The IAA also appears to arrest them. FIB shoots Haines, who kills Sanchez. This then devolves into the IAA and FIB opening fire on each other, but why? They both want custody of the same guy, a conflict that can be resolved without shooting at each other. And if Agent Norton's claim that the FIB are corrupt and on the IAA payroll is true, there's even less sense in this.
gpt
The FIB and IAA are rival agencies that are fighting for the same limited budget, financial and authority-wise. Sanchez and his superiors in the FIB wants Haines to be kept in-house so that they can cover up Haines' messes and not publicize that the FIB are actively bankrolling and protecting criminals to undermine National Security. The IAA wants Haines to prove otherwise. Go do the math.

Merryweather being there after being lured by Trevor just adds to the mayhem.