WHITE: That was the most insane f***ing thing I have ever seen. Why the f*** would Joe hire a guy like that?
We learn later why Joe would hire a guy like that. He's got to know that Blonde's a loose cannon, but he's extremely loyal to Joe. Eddie convinces Joe to hire Blonde for the diamond job because he's been "good luck" in the past. They trust Blonde so much that later, it's hard for them to believe that Blonde was the reason the heist was a disaster.
[Orange shoots and kills Blonde]
ORANGE: Listen Marvin, I'm a c—listen to me, Marvin Mash, I'm a cop.
Orange has to know that he could be in serious trouble for killing Blonde and will have to have to come up with a convincing story to explain why. However, his loyalty is to protect his fellow cop. We wonder what he would have done if other guys besides Blonde were still in the funeral home. Our guess? His loyalty to the operation (i.e., nailing Joe) would override his loyalty to Marvin. He's already been traumatized by seeing some fellow officers gunned down that day, but watching one being burned alive? (See: Orange You Glad You Aren't Mr. Orange)
EDDIE: The man you killed just got released from prison. He got caught at a company warehouse full of hot items. He could have f***ing walked. All he had to do was say my dad's name, but he didn't. He kept his f***ing mouth shut. And he did his f***ing time, and he did it like a man. He did four years for us. So, Mr. Orange, you're telling me this very good friend of mine, who did four years for my father, who in four years never made a deal, no matter what they dangled in front of him, you're telling me now that this man is free and we're making good on our commitment to him, he's just going to decide, out of the f***ing blue, to rip us off? Why don't you tell me what really happened?
Now we know why Joe hired a hothead like Blonde. Eddie believes that Blonde's loyalty was absolute. He didn't just talk the talk. As far as Eddie's concerned, that seals the deal that Orange is lying. Loyalty among criminals is most important when one of them gets caught. You've got to maintain silence and not give anyone up if you're caught, even to the point of taking the fall for someone else. If you do that, you'll be taken care of like Joe took care of Blonde in prison.
WHITE: Joe, trust me on this. You've made a mistake. He's a good kid. […] We're all real emotional. But you're barking up the wrong tree. I know this man. He wouldn't do that.
WHITE: [pulls a gun on Joe] Joe, if you kill that man, you die next. I repeat, if you kill that man, you die next.
White puts his life on the line for Orange, but his loyalty to Orange comes from a very different place than Eddie and Joe's loyalty to Blonde. It's coming from an emotional place; he has no reason to have faith in Orange based on Orange's behavior. This turns out to be a fatal flaw for White. Loyalty is in the act, not in the heart. Personal feelings or relationships have no place in this equation. See The Godfather, parts I, II, and III and every episode of The Sopranos. You have to kill your best friend if they cross you.
ORANGE: I'm a cop, Larry… I'm sorry. I'm so… so sorry. I'm a cop.
WHITE: [sobbing} Oh! Oh!
ORANGE: Sorry. I'm sorry. Sorry. Larry!
Why does Orange confess to Larry, knowing that it could get him killed? Tarantino has said that anyone who can't answer that question hasn't understood the film. We'll give you a minute. Okay. Orange tells White because it's the honorable thing to do to tell the truth to someone who's protected you, cradled you, killed friends for you, and risked his life for you. White refuses to leave Orange behind even though he could have taken the diamonds and left him there to die. White knows he's going to do some serious time when the cops get there. This guy deserved the truth, but he couldn't handle the truth. Why wait until now? Remember that Orange's first duty was to the police job—capturing Joe. Joe's dead, though, and the mission's over, so he won't be compromising anything by revealing his identity. Like White, Orange dies because of loyalty based on emotion.