Since the beginning of “DT” is a direct pick up from “Salvation”, Sam’s still on an emotional high after seeing the demon, nearly killing it, and insisting to Dean that he just needed to get back into the house and he could have killed it. Then Meg has John, and from this point on, Sam’s the calm, logical voice for the episode, while Dean is the barely-held together irrational voice. This is actually a slight twist on their relationship. Dean wants to use the Colt as a trade, but Sam is the one to voice the concern of, "if Meg wanted a trade, why didn't she mention one?" Sam sits and reads the Key of Solomon while Dean is all movement and action. Sam draws the protection symbols on the trunk of the Impala (THE CAR!), and insists that the Colt be left there for protection. Again, invoking logic where Dean is ready to go in guns blazing. When they find their father tied on the bed (mind drifts to the bad place for a moment...), it's Sam who invokes logic that they 'test' their dad to make sure he's not possessed.
Now, on this side, we have Dean, who has nearly violently insisted that John is still alive up until they actually find him.
Sam hesitated over finishing the exorcism, but Dean's determination pushed him on. What was Sam's reluctance? Did Sam honestly think a living demon was better than a dead, non-possessed girl? At what point are they "saving" an innocent, and at what point is it murder? Was that moral dilemma what made him pause?
Sam was partially conscious after getting the crap beat out of him by possessed!boy, but he was aware enough to see that Dean killed a human (possessed human, but nonetheless an innocent), in order to save his life. Even in the face of his brother's shooting of an innocent to protect him, Sam is calm, stating his thanks quietly. Dean appears to be barely holding it together, admitting he'll do "anything" for his family.
Now, if you take all these things swirling in Sam's mind when he walks into the room and sees Dean with the Colt on their father, shouldn't he have questioned Dean's sanity? He's watched Dean be pushed and stretched the whole episode, yet with barely-there hesitation, Sam slides behind Dean, siding with his brother over his father. Where did Sam's faith come from? It is because Sam knows that Dean and John were closer than Sam and John ever were? Was it Dean's words in "Salvation" in the hotel room (not worth dying over, and yes, I mean it! I hope we never find it!)? Was it "You're all I have," that broke through Sam’s single-mindedness?
That last look at Dean in the rearview mirror, then telling their father, "No sir, not before everything". Family, your living family, should be the most important thing. Faced with the reality of killing his father to destroy the demon that took Jess from him, finally snapped something inside Sam. What was he fighting for? Was it merely revenge? Was it worth their father's life? John thought so; it was all he could think of. Dean, though, his pleading not to shoot their father, even after being tortured by Demon!John (pausing...back), had to have hit something in Sam. But I do think it was seeing his father’s rage to kill him, to end it, that had Sam dropping the Colt. Sam saw himself in John, saw what could happen to him if he let revenge continue to be what fueled him. He couldn't kill himself, so he couldn't kill John, either. Sam looks so broken when he lowers the Colt. Was he thinking that if the demon took possession again, it would kill both Dean and him? It would run rampant, destroying more innocent families? Watching the thing with their father's face twist everything they'd known? It was almost a 'sorry', but Sam had to have known John would accept nothing other than his own death, if it meant killing the thing that destroyed their family.