I'm with Oli in this and in his previous post:

Let's say Michael did bring Fredo to Havana to test his loyalty. And, suppose the test was to tell Fredo that Roth planned to kill him, but he was going to strike first: "Hyman Roth will never see the New Year." If Fredo was the traitor, then he'd tell Roth--and Roth would, as Oli said, move up his plan to kill Michael first. So, the only way Michael would know that Fredo was the traitor would be in the instant before he died at Roth's hand.

I think everyone has posted thoughtful answers. Thanks! But I still can't find a logical explanation for why Michael told Fredo his plan to kill Roth.