Zevachim 13A

צד כרת לא פריך.

does not refute the inference by citing a common element of karet, as the elements of karet in a sin offering and in a Paschal offering are not parallel.

אשם נמי לייתי!

The Talmud asks: If so, let it be derived from this inference that a guilt offering is also disqualified if sacrificed not for its sake.

אשם ⁠– פריך: מה להצד השוה שבהן, שכן ישנן בצבור כביחיד.

The Talmud answers: With regard to a guilt offering, ben Azzai refutes the inference as follows: What is notable about the common element of a sin offering and a Paschal offering? It is notable in that there are communal offerings as well as individual offerings of these types, as well as communal burnt offerings, whereas there is no communal guilt offering.

ואיבעית אימא: צד כרת נמי פריך, ובן עזאי גמרא גמיר לה. והא דקאמר רב הונא קל וחומר ⁠– לא אמרה אלא לחדד בה תלמידיו.

And if you wish, say instead that actually, ben Azzai also refutes the entire inference, because a sin offering and a Paschal offering uniquely share an element of karet. And the reason ben Azzai maintains that a burnt offering sacrificed not for its sake is disqualified is that he learned it as a tradition. And as for the fact that Rav Huna cites an a fortiori inference, he does not believe it to be the true source for ben Azzai’s halakha; he said it only to sharpen the minds of his students with it, challenging them to refute it.

מתני׳ הפסח והחטאת ששחטן שלא לשמן, קבל והלך וזרק שלא לשמן; או לשמן ושלא לשמן, או שלא לשמן ולשמן ⁠– פסולים.

Mishnah: With regard to the Paschal offering and the sin offering, where one slaughtered them not for their sake, or where he collected their blood in a vessel, conveyed this blood to the altar, or sprinkled this blood on the altar not for their sake, or where he performed one of these sacrificial rites for their sake and not for their sake, or not for their sake and for their sake, in all these cases the offerings are unfit.