Why did Ben Azzai copy Rabbi Akiva?

Question

In today's Daf Yomi, Brachot 62a, it says:

It was taught in a baraita in tractate Derekh Eretz that Rabbi Akiva said: I once entered the bathroom after my teacher Rabbi Yehoshua, and I learned three things from observing his behavior: I learned that one should not defecate while facing east and west, but rather while facing north and south; I learned that one should not uncover himself while standing, but while sitting, in the interest of modesty; and I learned that one should not wipe with his right hand, but with his left. Ben Azzai, a student of Rabbi Akiva, said to him: You were impertinent to your teacher to that extent that you observed that much? He replied: It is Torah, and I must learn. Similarly, we learned in a baraita: Ben Azzai said: I once entered a bathroom after Rabbi Akiva, and I learned three things from observing his behavior: I learned that one should not defecate while facing east and west, but rather while facing north and south; I learned that one should not uncover himself while standing, but while sitting; and I learned that one should not wipe with his right hand, but with his left. Rabbi Yehuda said to him: You were impertinent to your teacher to that extent? He replied: It is Torah, and I must learn.

Clearly, both Rabbi Akiva and Ben Azzai knew that following one's rabbi into the bathroom was improper in general (with possibly a certain leniency to do it for learning Torah). After having already heard what Rabbi Akiva learned from following Rabbi Yehoshua, why did Ben Azzai feel the need to do exactly what his rabbi, Rabbi Akiva did, by following him - and in fact, ended up learning the exact same things?

Answer 1

If the second event is recorded in the Talmud, there must be a reason. One possibility is to teach us that we must check things out for ourselves whenever possible, and not take anybody's word for it, however high and mighty he might be. This can only reinforce our convictions, and must not be used as evidence of lack of trust in our sources.

Answer 2

This is addressed by R. Joseph Hayim of Baghdad in his commentary there:

ונראה לי בס"ד דכניסת רבי עקיבא אחר ר"י היה קודם שנכנס בן עזאי אחר רבי עקיבא וסיפור זה שסיפר רבי עקיבא על כניסתו אחר ר"י זה הסיפור היה אחר שנכנס בן עזאי אחריו ומ"ש לו בן עזאי כל כך העזת פנים אף על גב דגם הוא עשה כן עם כל זה א"ל כך לראות מה ישיב לו על זה אך סיפור שסיפר בן עזאי על כניסתו אחר רבי עקיבה היה אחר שסיפר רבי עקיבא על כניסתו אחר ר"י ובזה יתיישבו איזה דקדוקים במאמר הזה ודוק

And it seems to me with the assistance of Heaven that the entering of R. Akiva after R. Yehoshua was prior to the entering of Ben Azzai after R. Akiva. And this story that R. Akiva told about his entering after R. Yehoshua was after Ben Azzai entered after him. And that which he said to him "Ben Azzai, this much you have brazened" even though he also did so, notwithstanding this he said it to him to see what he would answer him on this. But the story that Ben Azzai told about his entering after R. Akiva was after R. Akiva told about his entering after R. Yehoshua. And with this a bunch of subtleties in this passage are resolved.

According to this, the premise of your question is incorrect. At the time that Ben Azzai followed R. Akiva into the bathroom he was unaware that R. Akiva had followed R. Yehoshua into the bathroom, and he was unaware of the three things that R. Akiva had learned on that adventure.