In the Mishna, Miqvaos 7:1, Rabbi Akiva quotes Rabbi Ishmael as having declared that snow does not count towards the completion of a mikva, but the people of Meibeba then testify that Rabbi Ishmael thinks that it does - in fact, that he even once had a mikva filled with snow from the outset:
אמר רבי עקיבא, היה רבי ישמעאל דן כנגדי לומר: השלג אינו מעלה את המקוה. והעידו אנשי מידבא משמו שאמר להם: צאו והביאו שלג ועשו מקוה בתחלה
According to both Tosfos Yom-Tov and Tiferes Yisrael (Yakhin), Rabbi Ishmael really did believe that snow counts towards the completion of a mikvah, and was advancing a contrary opinion for the sake of arguing only. In the words of the Tosfos Yom-Tov:
ואמנם מה שהיה חולק על ר"ע הוא במשא ומתן של הדין על צד הויכוח, לא שהוא יסבור כך
Concerning his disagreement with Rabbi Akiva, this was only in the give and take of the law and for the sake of an argument, and not because he actually thought this.
Tiferes Yisrael suggests the same thing (דרך פלפול בעלמא), but as the second of two possibilities - the first being that Rabbi Ishmael believed that snow doesn't count towards the completion of a mikvah and that he subsequently changed his mind. I prefer that suggestion myself, since it has Rabbi Ishmael arguing with sincerity, but am intrigued by the other.
Normally, I would have thought, if a person chooses to "play devil's advocate" they indicate to their opponent that this is what they're doing, but Rabbi Ishmael allowed Rabbi Akiva to walk away believing that this was actually his opinion. Are there any sources (obviously, aside from this one) that this is a respectable thing to do? That we can pretend to an opinion that we don't really have, purely for the sake of an argument?