Michael was never more reprehensible than at his boathouse meeting with Tom, Rocco and Neri near the end of II:

TOM: Why did you ask me if something was wrong when I came in?
MICHAEL: I thought you were goin' to tell me that -- you were going to move your family to Vegas -- and that you'd been offered the vice-presidency of the house and hotels there I thought you were goin' to tell me that.
TOM: I turned them down -- do I have to tell you about ever offer I turn down?
MICHAEL: let's do business.
TOM: Alright -- just consider this Mike -- that's all just consider it. Now ROTH and the Rosato's are on the run -- are they worth it? And are they strong -- is it worth it -- I mean you've won -- do you have to wipe everyone out?
MICHAEL: I don't fell I have to wipe everyone out -- just my enemies -- that's all. You gonna come along with me in these things I have to do -- or what. Because if not you can take your wife, your family, and your mistress -- and move 'em all to Las Vegas.
TOM: Why do you hurt me MICHAEL -- I've always been loyal to you -- I mean what is this.
MICHAEL: So -- you're staying?
TOM: Yes, I'm staying. Now what is it that you want me to do?

So: Why did Michael hurt Tom--humiliated him--in front of Rocco and Neri? I’m tempted to say, “because he could,” and it wouldn’t be a wrong answer. But I think Michael, as usual, had additional reasons.

What do you think?

Interesting Question. I think by that point Mike was so paranoid and thought everyone around him had ulterior motives. Just shows how far he came from the young man returning from serving his country and wanting nothing to do with the mob life

If memory serves me correctly, prior to that he had Tom appointed as the head of the family while Michael was away; there was that scene where Michael manipulated Tom by calling him his brother, which he definitely knew Tom always wanted to hear.

Perhaps Rocco or Neri complained to Michael about Tom, or on the other end of the spectrum, perhaps Michael saw Rocco and Neri listen more and more to Tom and he wanted to put him in his place.

Or maybe, as you say TB, because he could. But I always found that scene and their dynamic very interesting as well.

I think that he was bullying Tom in order to extract an unconditional pledge of loyalty from Tom. He needs Tom's support to go ahead with killing Fredo.

In the novel, when Tom is released by Solozzo and returns to the compound, Michael is a bit resentful when he realizes that Tom is closer to Sonny than he could hope to be. Perhaps it's a carryover of that?

Exactly. Mike never felt close to Tom. Remember the wedding reception scene after Mike introduced Tom to Kay. Mike felt it necessary to comment to Kay that Tom was not a Sicilian. Totally unnecessary.

Michael introduced Tom to Kay “My brother, Tom Hagen”

Then only after Kay asked,
Michael explained why and added,

The Elephant in the room — Tom is not a wartime consiglieri In fact not much of a peace time consiglieri either
even in routine simple matters, Michael had to guide Tom eg: Tom had no idea that Roth's passport's been invalidated except for return to the United States

• penultimate boathouse scene

I see it differently.... "boathouse meeting" was Tom's [self] punishment!

Tom asked the question "-- in front of Rocco and Neri"So Michael answered "-- in front of Rocco and Neri"

Then Tom was trying to discourage Michael from killing Roth — on the run now — but Roth will always be a threat to Michael
A man like Roth would never rest until Michael was dead or destroyed

• "The Art of the Deal" Trump style!

Michael giving brother! Tom a drink and making Tom the Don Well....'Band of Brothers'

How could Tom have not known about Frankie Pentangeli's survival?

• Tom lets his one and only client Michael commit up to five counts of perjury
• Tom had no idea “Alive -- Pentangeli is alive” until after Michael had committed perjury
• “Fredo says he doesn't know anything -- and I believe him”
• Then we find Fredo knew plenty

Besides, Tom sets himself up for [self] punishment! every time. Tom never learns.... among others,
1. penultimate boathouse scene
2. Ola meeting
3. Michael enlisting in the Marines
4. Fish tank scene

Tom doesn't read the situation and wouldn't let go.... even after the dreaded Corleone stare and the decision has obviously been made
Tom can't see that the decision made will remain unchanged and whatever Tom says will make no difference whatsoever

It is clear to everyone but Tom!

These are all excellent observations. The variety of them shows just how much nuance is contained in that brief scene. I'd like to add a few:

I'm usually far more sympathetic to Tom than to Michael. But, in this case I think Michael was legitimately pissed at Tom for several reasons. Michael was stunned and dismayed when he learned--after he testified--that Pentanageli was alive. Tom's reply was insulting: "Roth, he played this one beautifully...you've opened yourself to five counts of perjury." Tom was praising Roth and chiding Michael. Not very "brotherly."

Tom over-reacted to Michael's order to kill Roth ("It'd be like killing the President...do you have to kill everyone?"). That type of lawyerly over-caution might have been necessary for Sonny, given his hot temper, but not for Michael, who'd correctly thought it through and concluded that Roth was his most resourceful and dangerous enemy, and had to go.

Tom had also had let Michael down badly by screwing up. "Our people with the NY detectives said [Pentangeli] was half deadI, scared.talking out loud about how you betrayed him..." If Tom did his job right as Michael's liaison with the NY detectives , why didn't he pick up that Pentangeli survived before Michael testified? And, when Michael asked, "What abot Fredo?", Tom, who was Michael's liaison to Fredo replied, "He says he knows nothing--and I believe him." But, Fredo knew Pentangeli had survived--and, more important, that the Senate lawyer, Questadt, "belongs to Roth." Why didn't Tom get that out of Fredo before Michael testified?

Michael needed Tom for two critical missions at that point: To persuade Vincenzo to come to America to show himself when Pentangeli testified, and to persuade Pentangeli to kill himself. He had accumulated doubts about Tom's attitude toward him and his judgment, That's why he got tough and hurtful when he asked, "Are you going to come along with me in these things I have to do?"

When Michael says to Tom: "...you can take your wife, your family and your mistress to Vegas..." the camera pans to Neri, whose smug, self-satisfied expression tells me that he was the source of that tidbit.