he found out Vanille's secret and almost straight up murdered her.  Let's think about this for a second...

1.  He's been travelling with Vanille and become friends with her.

2.  Vanille didn't do anything in the video he was shown, Fang did.

3.  Fang had no way of knowing what would happen to his son.

4.  Fang didn't actually do it to his son, that Fal'Cie did.

But it's okay, Sazh decided at the last minute that he shouldn't shoot Vanille in the head because...she's a teenager.  Yes, that is why you shouldn't murder your friend.  Good job.  Surely you are the voice of reason.  And did you notice how quickly he got over it and went back to being friends with her after wanting to kill her?

It was frustrating because up to that point in the story, Sazh had been the voice of reason.  What I half-expected, what would have happened if the writing were actually good, was for Sazh to take the gun, act like he was going to chase Vanille down and kill her, and then find her and say, "Come on, Vanille.  We got to get the fuck out of here."