Zevachim 82A

וניתיב לפנים והדר ניתיב לחוץ? כיון דאיכא חטאת ואשם דכי נכנס דמן פסולין, לא פסיקא ליה.

And if you suggest that the priest should first place blood from the mixture inside the Sanctuary and again place blood outside, on the altar, although this resolution is applicable to most offerings whose blood is placed outside, nevertheless the tanna of the Mishnah chose to omit this case. The reason is that since there are a sin offering and a guilt offering, concerning which, according to the opinion of R' Eliezer, when their blood enters the Sanctuary they are disqualified from being placed on the external altar, the tanna could not teach this halakha categorically. In other words, as the tanna could not issue a categorical ruling that applies to all types of offerings, he omitted the opinion of R' Eliezer here.

שהיה רבי עקיבא אומר [וכו׳]. אמר רב יהודה אמר שמואל: משל למה הדבר דומה? לתלמיד שמזג לרבו בחמין, ואמר לו: מזוג לי. אמר לו: במה? אמר לו: לא בחמין אנו עסוקין עכשיו?! בין בחמין בין בצונן.

§ The Mishnah teaches that R' Akiva would say: Any blood that is to be presented outside that entered to atone in the Sanctuary is disqualified. The Talmud discusses the source for R' Akiva’s ruling. The verse states: “And any sin offering, whereof any of the blood is brought into the Tent of Meeting to atone in the Sanctuary, should not be eaten” (Leviticus 6:23). How does R' Akiva apply this halakha to all offerings whose blood is presented on the external altar? Rav Yehuda says that Shmuel says: Hear a parable: To what is this matter comparable? To a student who mixed wine with hot water for his teacher. And the teacher said to him: Mix another drink for me. The student said to him: With what should I mix the wine, hot or cold water? The teacher said to him: Aren’t we dealing with hot water? Now that I requested that you mix me another cup, I mean that you should mix it either in hot water or in cold. Otherwise, the teacher would not have needed to say anything.