"And he shall bring his guilt offering which he has sinned" (Leviticus 5:7). He brings two and does not bring one. Is this not a matter of logical inference? This person brings according to his means and the leper brings according to his means; just as the leper brings one in place of one, so too this person - since his rich-man's offering brings one - should have his poor-man's offering bring one as well. Scripture therefore teaches, saying, "two turtledoves or two young pigeons": he brings two and does not bring one. One bird is for a sin offering and one is for a burnt offering, and the sin offering takes precedence over the burnt offering. The burnt offering is brought from the same species as the sin offering. And if he brought his sin offering and then died, his heirs bring his burnt offering.
Why the Poor Bring Two Birds for Atonement
Yalkut Shimoni on Torah 473:5
וְהֵבִיא אֶת אֲשָׁמוֹ אֲשֶׁר חָטָא וְגוֹ'. שְׁנַיִם הוּא מֵבִיא וְאֵינוֹ מֵבִיא אֶחָד. וַהֲלֹא דִין הוּא, זֶה מֵבִיא בְּהֶשֵּׂג יָד וּמְצֹרָע מֵבִיא בְּהֶשֵּׂג יָד, מַה מְּצֹרָע אֶחָד תַחַת אֶחָד אַף זֶה הוֹאִיל וְעָשִׁיר שֶׁלּוֹ מֵבִיא אֶחָד יְהֵא עָנִי שֶׁלּוֹ מֵבִיא אֶחָד, תַּלְמוּד לוֹמַר "שְׁתֵּי תֹרִים אוֹ שְׁנֵי בְנֵי יוֹנָה", שְׁנַיִם הוּא מֵבִיא וְאֵינוֹ מֵבִיא אֶחָד. אֶחָד לְחַטָּאת וְאֶחָד לְעֹלָה, שֶׁתַּקְדִּים חַטָּאת לְעוֹלָה. שֶׁמִּמִּין חַטָּאת יָבִיא עוֹלָה, שֶׁאִם הֵבִיא חַטָּאתוֹ וּמֵת יָבִיאוּ יוֹרְשִׁים עוֹלָתוֹ.