I totally understand the value of being effective over being right, but I would like some help figuring out how/if to apologize in this situation.
During a recent meeting involving my manager and all of his direct reports (all lawyers), everyone was asked to share what they are working on, roundtable style. After I finished my brief sharing session, my boss specifically asked me to elaborate about a current project I am working on, which is highly confidential. He has also been involved in the work and is transitioning some of it over to me.
In response, I said "Isn't that project confidential?" He told me I could share it with this group, but something did not feel right about it so I told him that I would be more comfortable if he shared the details. Perhaps it was just my inexperience with this situation, but I was very uncomfortable. He visibly rolled his eyes and then briefly explained what I was working on to the group.
My gut tells me that I should apologize for questioning him in front of the rest of his directs and not seeing an opportunity he was giving me to "show off" some of what I was going. On the other hand, I am really wondering if sharing information about a confidential project was the professional thing to do.
Thoughts? Advice? Tips on how to apologize if you think I should?

Get feedback first
Sounds like you directly challenged his right as the boss to decide how to handle confidential issues in his meetings. On the face of it, not good, and you probably should have done as he asked. Especially after you raised the confidentiality issue and he clarified that he thought it was appropriate for you to discuss that matter in that meeting.
Of course there could be all kinds of details that might mean that he made a poor judgment, or that you needed more of a steer from him about what information could appropriately be revealed. You can't discuss these details here (confidentiality!), so you'll have to reflect on whether you were being insubordinate or ethical, or whether you can't currently figure out where you went wrong. Then I suggest that:
Sure...
You could probably apologize. I don't think it's as big a deal as you think it was. If i had been your boss I probably would have rolled my eyes, because what happens in my meeting is my call. Your boss assumed yu would figure out that his asking you overruled any concerns you might have had.
And, when it comes to confidentiality, it's not wrong to be a little bit more careful...so, maybe you want a bit too far but I can understand why you paused.
Let it go. If you think apologizing would help, do so, then let it go.
Mark