Admitting an Error

Rav Ya’akov Ades, shlit”a, the Rosh Yeshivah of Kol Ya’akov, once recounted the following:
Rav Shlomo Zalman Auerbach, zt”l, related that the administrators of Kol Torah requested that he give a shiur to determine if he was the worthy of becoming the Rosh Yeshivah. As he was giving his first shiur, Rav Yonah Marzbach, zt”l, one of the Roshei Yeshivah, asked him a very penetrating question on the very foundation of his argument. Although Rav Auerbach immediately thought of three ways to answer his question, in his heart he felt that perhaps Rav Marzbach was right and his underlying premise really was faulty. So he simply said, “I was mistaken,” and sat down.
When he went home and his wife asked him how it went, he replied simply, “I tripped up.”
Rav Shlomo Zalman, concluded, “Until this day, the administrators never informed me whether my shiur was considered a success or not...”
Years later, Rav Yonah Marzbach also recounted the very same incident. “The moment he publicly admitted his mistake I decided that he should be our Rosh Yeshivah. Someone who is able to say, “I was wrong,” in a public shiur before the Yeshivah, during his very first shiur yet, deserves to be our Rosh Yeshivah. This is the exactly the kind of person we were looking for!”
On a different occasion they asked Rav Chaim Brisker, zt”l, if a certain very erudite scholar was eligible for a certain prestigious position. To their surprise, Rav Chaim immediately responded that he was not. When asked why this man was not qualified, Rav Chaim explained, “In order to be worthy of being a Rosh Yeshivah or the like one must be willing to step down from a shiur if mistaken. It is true that your candidate is very erudite, but I don’t believe he has the character to step down if mistaken. So this position is not for him…”