DON CORLEONE: So, Barzini will move against you first. He'll set up a meeting with someone that you absolutely trust, guaranteeing your safety. And at that meeting, you'll be assassinated.
Don Corleone is relying on pure criminal intuition here. He's going with his gut, and he's completely right. He's been around lies and deceit for so long that he can always sense the pattern. Without this advice, Michael could well have been assassinated.
DON CORLEONE: Listen, whoever comes to you with this Barzini meeting, he's the traitor. Don't forget that.
This is more evidence of Don Corleone's great nose for lies. Maybe it's true that only a great liar would himself be able to recognize another?
MICHAEL: […] Only don't tell me that you're innocent. Because it insults my intelligence and it makes me very angry. Now, who approached you first? Barzini or Tattaglia? CARLO: It was Barzini. MICHAEL: Good. There's a car outside that will take you to the airport. I'll call your wife and tell her what flight you're on.
Michael is deceiving Carlo, after the violent deception Carlo helped Barzini play. But there's a practical reason for this too: It makes it much easier to kill Carlo. If he thinks he's going to survive, he won't put up much of a fight. They'll be able to murder him more efficiently.
TESSIO: Tell Mike it was only business. I always liked him.
Michael observes that Tessio turned traitor because it seemed like the smart thing to do. He doesn't really blame him for it, and Tessio doesn't really blame Michael for killing him. From both of their perspectives, it really is "just business."
CONNIE: Why do you think he kept Carlo at the mall? All the time he knew he was going to kill him. And then he stood Godfather to our baby. You think you know your husband? You know how many men he had killed! Read the papers. Read the papers! That's your husband!
Of course, Connie's husband also helped murder her own brother, in addition to beating her. So, Michael, by his code anyway, needed to kill him. (There might be better reasons for thinking Michael is a monster than this one, though.)