Another interpretation: what does Scripture teach by saying "one for a sin offering and one for a burnt offering"? One might have thought that since the two come in place of one, both should be a sin offering. Scripture therefore teaches, saying, "one for a sin offering and one for a burnt offering" - the two are not both for a sin offering, and they are not both for a burnt offering, but rather one is for a sin offering and one is for a burnt offering. "And he shall bring" - that the owners should designate them, one for a sin offering and one for a burnt offering. From where do we learn that if the priest designated them, his designation is valid? Scripture teaches, saying, "one for a sin offering and one for a burnt offering." "And he shall bring them to the priest" - "and he shall bring," even after the Day of Atonement. "Them" - teaching that a bird offering has no redemption. "To the priest" - teaching that the owner is responsible for the trouble of bringing them.
Designating One Bird for Sin and One for Ascent
Yalkut Shimoni on Torah 473:6
דָּבָר אַחֵר מַה תַּלְמוּד לוֹמַר "אֶחָד לְחַטָּאת וְאֶחָד לְעֹלָה", שֶׁיָּכוֹל הוֹאִיל וּשְׁנַיִם בָּאִין תַּחַת אֶחָד יִהְיוּ שְׁנֵיהֶם חַטָּאת, תַּלְמוּד לוֹמַר "אֶחָד לְחַטָּאת וְאֶחָד לְעֹלָה", וְאֵין שְׁנֵיהֶם לְחַטָּאת וְאֵין שְׁנֵיהֶם לְעוֹלָה אֶלָּא אֶחָד לְחַטָּאת וְאֶחָד לְעוֹלָה. וְהֵבִיא, שֶׁיַּפְרִישֵׁם הַבְּעָלִים אֶחָד לְחַטָּאת וְאֶחָד לְעוֹלָה. מִנַּיִן שֶׁאִם הִפְרִישָׁם הַכֹּהֵן הֶפְרֵשׁוֹ הֶפְרֵשׁ, תַּלְמוּד לוֹמַר "אֶחָד לְחַטָּאת וְאֶחָד לְעֹלָה". וְהֵבִיא אֹתָם אֶל הַכֹּהֵן. וְהֵבִיא, אַף אַחַר יוֹם הַכִּפּוּרִים. אֹתָם, שֶׁאֵין לָעוֹף פִּדְיוֹן. אֶל הַכֹּהֵן, מְלַמֵּד שֶׁחַיָּב בְּטִפּוּל הֲבָאָתָם.