Another interpretation: "a lamb for a house" teaches that a person brings and slaughters on behalf of his minor son and daughter, and on behalf of his Canaanite slave and maidservant, whether with their knowledge or without their knowledge. But he does not slaughter on behalf of his adult son and daughter, nor on behalf of his Hebrew slave and maidservant, nor on behalf of his wife, except with their knowledge. If one set aside a Passover lamb on behalf of another, he has accomplished nothing. "A lamb for a house" is not a Torah-level requirement, as we learned: One who says to his children, "I am slaughtering the Passover on behalf of whichever of you goes up first to Jerusalem"—once the first one has brought in his head and the greater part of his body, he has acquired his portion and confers it upon his brothers with him. Now if you say "a lamb for a house" is a Torah-level requirement, it rests on the actual meat and he confers it on them; then why did their father say it to them? In order to spur them on [to the commandments]. It was also taught thus: There was an incident in which the daughters got there ahead of the sons, and the daughters were found to be eager and the sons sluggish.
Slaughtering the Passover for Children and the Eager Daughters
Yalkut Shimoni on Torah 192:3
דָּבָר אַחֵר, שֶׂה לַבָּיִת מְלַמֵּד שֶׁאָדָם מֵבִיא וְשׁוֹחֵט עַל יְדֵי בְּנוֹ וּבִתּוֹ הַקְּטַנִּים, וְעַל יְדֵי עַבְדּוֹ וְשִׁפְחָתוֹ הַכְּנַעֲנִים בֵּין מִדַּעְתָּן בֵּין שֶׁלֹּא מִדַּעְתָּן, אֲבָל אֵינוֹ שׁוֹחֵט עַל יְדֵי בְּנוֹ וּבִתּוֹ הַגְּדוֹלִים, וְלֹא עַל יְדֵי עַבְדּוֹ וְשִׁפְחָתוֹ הָעִבְרִים וְלֹא עַל יְדֵי אִשְׁתּוֹ אֶלָּא מִדַּעְתָּן. הִפְרִישׁ פֶּסַח עַל חֲבֵרוֹ לֹא עָשָׂה כְּלוּם. שֶׂה לַבַּיִת לָאו דְּאוֹרַיְיתָא דִּתְנַן הָאוֹמֵר לִבְנוֹ הֲרֵינִי שׁוֹחֵט אֶת הַפֶסַח עַל מִי שֶׁיַעֲלֶה מִכֶּם רִאשׁוֹן לִירוּשָׁלַיִם כֵּיוַן שֶׁהִכְנִיס רִאשׁוֹן רֹאֹשׁוֹ וְרֻבּוֹ זָכָה בְּחֶלְקוֹ וּמְזַכֶּה אֶחָיו עִמּוֹ, וְאִי אַמְרֵת שֶׂה לַבָּית דְּאוֹרַיְיתָא עַל בִּישְׂרָא קָאי וּמְזַכֵּי לְהוּ אֶלָּא לָמָּה לְהוּ דְאָמַר לְהוֹן אֲבוּהוֹן כְּדֵי לְזָרְזָן [בְּמִצְוֹת]. תַּנְיָא נַמִי הַכִי, מַעֲשֶׂה הָיָה וְקָדְמוּ בָּנוֹת לְבָנִים וְנִמְצְאוּ בָּנוֹת זְרִיזוֹת וּבָנִים שְׁפָלִים.