Well, I would argue they didn't. Others think that Michael did, but then brought him back in after Vito died.

One thing is sure about that particular meeting. Lies were told, the biggest one being that Michael was making Carlo his right hand man in Vegas. Now Tom and Vito had to know this was a ruse. Even before Carlo set Sonny up, in fact on Carlo's wedding day Vito instructed Tom to give him a living, and to NEVER discuss the family business with him. So from the beginning nobody trusted Carlo. I have often thought that this may have been instrumental in Tessio's betrayal, after all with the family on the run, Tom being moved out, and Carlo being named Michael's right hand man I'd be scared if I was Tessio.

Michael wanted Tom "out" for reasons I have explained in this thread. Vito told Tom he was a good consigliere, but that there were things that he did not need to be a part of. Those "things" of course were the plans to kill off the heads of the other families. Tom would have not been of much use in this planning. Michael had brought in his own people, Neri and Rocco to be instrumental in this, and even though Tom knew about the secret Rocco regime, he would not have been of any use in planning this.
Tom would have argued against killing Cuneo and Stracchi for sure. Probably Green too. He would be gaming out everything that could possibly go wrong, and they didn't need that at the time.
Tom - Michael, just hear me out. We get Barzini. We get Tattaglia. Cuneo and Stracchi will fall into line. Why bother with them?
Michael - They were in on it with Barzini from the beginning. They are as guilty of killing Santino as barzini is.
Tom - and what about Moe Green? He'll fold in a heartbeat once he sees Barzini has been moved out.
Michael - You surprise me Tom. Moe Green doesn't need Barzini, he has support in Miami, and he'll run there for cover unless we get him first.
Tom - Do you want to wipe everyone out?
Michael - No. Just my enemies.


Still, when push came to shove, Tom instinctively knew there would be a traitor, and he asked Michael if he knew how they were going to come at him. So with that how "out" was he?

I think once Tom saw the way Michael treated Moe Green he pretty much knew that Green's ability to 'tawk" to Barzini wasn't going to make much difference.