Because they didn't fire him. They alienated him and made him look like someone that nobody could get along with to the boss and the boss fired him.That statement is simply wrong. They did try to fire him. You must have been getting a sandwich when Project Manager Pepe was shown talking to Brent alone, and informed Brent that the team voted to send him home as a result of what Stacy said. Brent was stuck having to argue the obvious-that only Donald Trump can send him home, the team was totally out on a limb.
It was a very key scene. It illustrated that in regards to Brent, the team had left the bounds of reality and had become an ignorant lynch mob.
This is what is so horrifying about Synergy. These people are college graduates and presumably well above average in intelligence and general ability, yet once the ball started rolling against Brent, nobody had the guts or ability to stand up and make this group realize that they were going way, way too far.
In addition to being factually incorrect, you also have conveniently neglected to give any examples of where Brent was obnoxious, outside of the time that he confronted Stacy in regards to her rudeness. Personally, I think Brent could have handled that better-but it was hardly that far over the line.