The Gemara earlier (3b) relates that Rebbe was studying a certain Tractate, and Rav asked him about a certain halacha in Hilchos Shabbos, which bore no direct relevance to the Tractate that Rebbe was studying. R' Chiyya who was present rebuked Rav saying: "Have I not told you before not to ask a question from another Tractate? - For had Rebbe not been so astute, he may have answered incorrectly, etc."

According to our Gemara, a Talmid Chacham must be able to answer any halachic query at any time, so why was Rav's behavior considered inappropriate?

Rav Y. L. Herzog zt"l answers that there is a difference between a question asked in private and a question asked in public.

It is true that an authentic Talmid Chacham must be fully versed in all halachic aspects, but, being human, even an experienced scholar can err or forget. Therefore, since there is a small chance that a Talmid Chacham may not be able to answer a given question, and considering the extreme severity of embarrassing another Jew in public, only questions pertaining to the Tractate being learned at the time should be asked in public.