Why did Michael Corleone not forgive his brother Fredo?

One of the major themes of "The Godfather 2" is Michael's transition from a kind man to a hardened, business-like criminal. Therefore, his treatment of Fredo by this time is "strictly business". Fredo has to be considered a threat to the Corleones after his betrayal, which is why Michael has him killed.

If you are still unconvinced, remember that this kind of behavior is not new to Michael; in "The Godfather," he kills Connie Corleone's husband after he betrays Michael to Don Barzini, even after he apparently forgives him.

EDIT: See the comments below. They make good points, though I'm pretty sure the Carlo is very much a part of the family and both Fredo and Carlo betrayed the family in a similar way.

Fredo inadvertently gave Michael's enemies the information AND action to assassinate Michael. Fredo gave out crucial details about Michael's routines. Someone opened the drapes that allowed a clean shot through Michael's bedroom window. It was only his instinct that allowed him to figure out just in time that the drapes were opened by someone who had no reason to do so or even to be in his bedroom alone.

As to the question, a more forgiving man would have forgiven Fredo -- and have him watched all the time. But let's make no mistake: If you are that stupid/naïve, you can and probably will be duped in the future. And next time, Michael may not figure it out in time.

And of course, Michael is not a forgiving man. I forget in what movie it was, but Michael once wondered why it was that he was so feared. It was precisely because Michael does not forgive. He does not forget. And he gets even.

So Michael killed his brother, making his son hate him. He killed his brother-in-law, making his sister hate him for quite a few years.

I'll add my two cents. In The Godfather (1972) After Fredo took Moe Greene's side when Michael confronted him about casino and hotel buying out Michael warned Fredo never to take sides against the family:

Michael: Freddie, you're my older brother. I love you. But don't ever take sides with anybody against the Family again. Ever.

Fredo didn't listen to it. Ignored the warn and colluded with Johnny Ola and Hyman Roth, which almost ended by Michael's death.

Even though Fredo didn't want Michael to be killed he probably knew that it was going to be a kidnapping. According to original screenplay by Mario Puzo and Francis Ford Coppola:

Michael: I want you to reach Fredo. I know he's scared, but have one of our people reach him. Assure him that there will be no reprisals. Tell him that I know Roth misled him.

Hagen: My information is that Fredo thought it was a kidnapping. Roth assured him nothing would happen to you.

Allowing "kidnapping" was not so innocent action. Fredo was OK with that.

Taken from answer of @paul: What exactly did Fredo do to betray Michael?

At this moment Michael was precautious cold-blooded criminal that protected himself and his family.

It was only in The Godfather: Part III many years later when Michael Corleone probably regretted killing his own brother. When speaking to Cardinal Lamberto:

Cardinal: Go on, my son.

Michael: I killed -- I ordered the death of my brother. He injured me. I killed my mother’s son. I killed my father's son. (he breaks down in tears)

Video fragment: The Godfather: Part 3 (7/10) [youtube]

Also when Michael had a stroke he was yelling for Fredo, probably crying out for forgiveness.

Video fragment: The Godfather - Never Let Anyone Know What You're Thinking [youtube]

Great answers here, but I'm going to add a simple, time-tested phrase to them:

You're only as strong as your weakest link.

Fredo, while good-intentioned, was dim-witted. Michael obviously loved his brother and trusted him, as with the fact that he allowed his children to go fishing with Fredo. He knew Fredo would never intentionally betray him again, but that didn't eliminate the idea that Fredo was weak and dumb, and could eventually be exploited again somehow in the future.

Michael from an ordinary man turned to cold-blooded murderer. He had lost feelings of pity and compassion. Any feeling of empathy was gone since the moment of murder attempt on his father, death of his brother Sonny and his wife Appolonia. All his human feelings atrophied. He became suspicious and cold to everyone, even his family members. He was cold to his wife, he was cold to Tom, he was cold to Fredo.

Michael as a Don is contrasted to his father Vito. Vito since his youth to old age was always kind, fair and generous. He loved greatly all the family's members. If place Vito on Michael's place regarding Fredo's betrayal, he would never kill his brother, even for so many mistakes. Michael turned to heartless criminal and considered his safety as most prioritized matter.

I looked through the other answers and this seems to be missing: In either the book or the movie (perhaps Saga) Michael says or thinks, that the problem is not forgiving Fredo but that it is Fredo forgiving himself -- he feels that Fredo will never do this. Implicitly, this makes him dangerous since his self-hatred might be turned outwardly. I can sort of see this.

However, if Michael was being completely pragmatic, why did he wait for his mom to die? If Fredo was indeed dangerous, then killing him asap would be the way Mike would have gone, I think.

I don't think it's a matter of forgiving Fredo. Michael had to kill Fredo because he can't let anyone do what Fredo did and not take appropriate action. I am reminded of speeches from two other movies that articulate this point well:

1) In "The Sting," Doyle Lonnegan explains why he can't give up and tracking down and killing small-timer Johnny Hooker. It's because if his childhood friend/rival finds out that he let Hooker get away with ripping him off, he'd have to kill that rival. He can't allow anyone to get away with going against him.

2) In "The Maltese Falcon," Sam Spade explains to Brigid why he has to turn her over to the police for killing Miles. He didn't think much of Miles, but because Miles was his partner, and if your partner is murdered, you simply have no choice but to do something about it. It was even more important than his own love for Brigid.

That's why Michael had to kill Fredo in the end, even though Fredo was never going to be a threat to him, and Fredo was probably forgiven by Michael. It's the principle behind it. Michael didn't articulate his principles the way Doyle and Sam did in those other movies, but it's the same thing. It's his consistent M.O. No matter how long he has to wait, he always kills whomever has betrayed or attacked the family. He waited until their mother was dead because he was also principled enough to take her into consideration.

Just before Mikael says the famous quote easy to find on YouTube, saying "you are not my brother", there are explanations.

And Mikael is under trial. And he asks Fredo if he can tell him something about the investigation. And Fredo says that the Senate lawyer Questadt belongs to Roth. It it seems like Mikael feels betrayed again. For example Pantageli was tricked by Roth to believe that Mikael tried to kill him so that he can testify at court against Michael (funnily he will do the opposite since he is an oldie friend of Vitto and his brother is present at the court maybe as a threat or reminder of good care of him). And probably that Fredo does not say enough there. Maybe he expected that Mikael will lose the trial and get more place in the family and the mafia clans. That is what is awesome about this film. So many returnings of what we believe. You really have to dig deep to explain. I also think Fredo does too much the tough guy in the video above. Mikael is not impulsive and disliked it.

Fredo Corleone's concealing of Questadt's allegiance was part of the reason why he was expelled from the Corleone family.

(source)

I think there are several possibilities, not mutually exclusive. The one that is raised most often here is Michael's hard-heartedness after his transformation is complete by the end of Part II. But I think that's only one part of the puzzle.

Remember that "mafioso" literally means "men of honor." Michael has so tightly integrated the code of honor (so far as it goes in that closed criminal world) of the mafia that he will not forego procedure.

While the book is not canon to the film, it does give hints as to the state of mind of Puzo (and by extension that of close collaborator Coppola) with respect to these characters. To this end, then, let us ponder Tom Hagan's page-side explaination as to why Michael had killed Carlo and Tessio - despite having already incapacitated those who would have pushed them to betray the family and being particularly fond of this latter - and ponder whether the same might not apply to Fredo:

"[T]reachery can't be forgiven. Michael could have forgiven it, but people never forgive themselves and so they would always be dangerous. Michael really liked Tessio. He loves his sister. But he would be shirking his duty to you and his children, to his whole family, to me and my family, if he let Tessio and Carlo go free. They would have been a danger to us all, all our lives."

By analogy, I propose that Michael killed Fredo above all because his beliefs dictated that in such circumstances there was simply no other choice. Perhaps it is debatable whether the prospect of letting his own blood would have made him rethink his values had he not been so coldhearted, and this I think is where Michael's transformation might be pertinent.

When Jonny Ola calls Fredo after the assassination attempt Fredo says, " I'm in deep enough already"..."you guys lie to me".. Meaning that he didn't expect them to try to kill Michael. However, he was in on the set up. Fredo was definitely the one who killed the Assassins because they were killed right outside of his house. His wife comes out screaming,"Mikey they're dead, right at my window they're lying there dead." Looking back I've been enlightening a bit. At first I thought Fredo had nothing to do with it. Accept talkingto Ola and Roth. However, while he was having a drink with Mike in Havana, you can see his remorse when he says "Mikey, I was mad at you, why we didn't spend time like this before!" At the Fredo was upset saying "He said it was something in it for me on my own..." "Your my kid brother, you take care of me? You ever think about that ever once think about that?"He goes on about bring stepped over in line to the thrown of being a Don by his father and he didn't want it that way. He also talks about people thinking he's dumb and him being treated like an earn boy. He says, "I'm smart and I want respect!!" I believe that Fredo gave Roth information about Mike's comings and goings and unknowingly gave too much information about the layout of the estate. I think he was left out of business part on both sides from both Mike and Roth. Besides the promise of getting something of his own after it's all over. In my opinion Fredo was shocked about the assassination attempt and nervously killed the Assassins outside his house. As Mike mentions to Tom, "Unless I'm very very wrong they're dead already, killed by someone close to us. Inside. Very frighten and botched." (FREDO) I'm not sure if Fredo opened the blinds or one of the Assassins did because if you didn't know they were going to kill him why would you open the blinds? I saw in an early comment that the original script had Mike being kidnapped. If that's the case then Fredo opened the blinds and helped the Assassins through security. Well we know Fredo helped them through security. I think him being weak and dumb Roth used that to his advantage to pull off the whole assassination attempt leaving Fredo in the dark for the bulk of it.