Main Question: I understand the first scenario where Raban Gamliel asked who the eighth person was in the Beis Din and that he should get out because they needed an odd number, and therefore there was justification for calling out that individual. However, I'm having difficulty understand the scenario of Rebbi asking about the Reiach Shum. What's the justification for Rebbi asking the question in the first place?

Side points:

Meaning, either one of a few things happen, no one gets up or the wrong person gets up, (both resulting in the smell remaining), or the guy who ate the garlic gets up and thus Rebbi would have been the cause of embarrassment. And in a piece of Gemara where the lesson is that one should not embarrass another, as well as that one should learn Davka from his Rebbi how to treat others, it is certainly not thematic that Rebbi would ask a question with possible ramification...

If perhaps one couldn't learn because of the smell (which is unlikely because as far as I know it's only because of Tzoah or something clearly disgusting that one cannot learn) we see in the Maharsha it's better to be Mevatel Torah than to be Mevayesh a Yid. If indeed the smell is Me'akev the learning, and therefore Rebbi could be justified in asking the person to leave, are we saying it's worth being îáééù a Yid to continue learning? For sure not!

Also, we see from the Ma'aseh of Rebbi Meir that one could be Matriach the Kelal, as I'm sure everyone giving a Get to this woman accomplished, in order to save the embarrassment of a yid...So Rebbi could perhaps have moved the Shiur outside where the smell wouldn't be as potent.

Ben Greene, Oak Park