At the end of S3E20 ("Death Benefit"), and made clear in S3E21, Finch peaces out for a while. Why does he do this?
He stated he'd be out if Reese killed the senator, but near the very end of that episode it's made clear that Reese did not kill the senator, as we see him talking on the phone in the car (and with no visible injuries) giving the go-ahead for Samaritan.
So then why did Finch leave?
My only guess:
We did see the senator's body in the house when the SWAT team moved in, that with the music seemed to want to lead us to believe, at least for a while, for dramatic effect, that Reese did kill him even though he didn't. But it was unclear to me what happened during that time, or what state the senator's body was in, or anything about that whole sequence, really.
The only thing I can think of is that Reese shot the senator but did not kill him, and that Finch believed Reese killed him, so he left. It's unclear and ambiguous, though, we never see Reese fire the gun, we only see him think about it.
So Reese shooting the senator and Finch believing it is only a wild guess. Nothing really supports or contradicts this (well, there is one contradiction: based on Reese and Finch's relationship as friends you'd think Reese would've told Finch that he didn't kill the senator, instead of letting Finch believe that he did then being all sad and surprised about Finch not being around later). But still I can't figure out why Finch left.