If these are the matters, we can proceed. The Midrash Tanchuma reveals to us the eulogy that Avraham Avinu gave for Sarah. The Midrash says: הִתְחִיל אַבְרָהָם לִבְכּוֹת עָלֶיהָ וְלוֹמַר, אֵשׁ ֶת חַיִל מִי יִמְצָא. בָּטַח בָּהּ לֵב בַּעְלָהּ . אֵימָתַי? בְּשׁ ָעָה שׁ ֶאָמַר לָהּ: אִמְרִ י נָא אֲחֹתִי אָתְּ. גְּמָלַתְהוּ טוֹב וְלֹא רָע כֹּל יְמֵי חַיֶיהָ. דָּרְשׁ ָה צֶמֶר וּפִשְׁתִּים, בֵּין יִצְחָק לְיִשְׁמָעֵאל, שׁ ֶאָמְרָה, גָּרֵשׁ הָאָמָה הַזֹּאת וְאֶת בְּנָהּ.
Avraham began to cry for her, and to recite: "A woman of valor, who can find one? Her husband's heart trusts in her" - when was this? When he said to her "Say that you are my sister." "She repays his good, and not his bad, all the days of her life. She susses out linen and cloth" - this is between Yitzchak and Yishmael, when she said, "kick out this maidservant and her son."
The Etz Yosef comments: It is possible that wool hints at Yitzchak as a righteous person – in reference to Yom Kippur, when our sins are transformed from red as scarlet to white as wool. Flax hints at Yishmael, as found in Sefer Yeshayahu (5:18): הוֹי מֹשׁ ְ כֵי הֶעָוֺן בְּ חַבְ לֵי הַשּׁ ָוְא וְכַעֲבוֹת הָעֲגָלָה חַטָּאָה – Woe to them that draw iniquity with cords of vanity, and sin as it were with a cart rope, or as it is stated earlier in Bereishit with regards to Kayin bringing flax seed as his offering, while Hevel brought from his livestock (wool). Therefore, wool and flax are considered sha’atnez – prohibited from being mixed together. Hakadosh Baruch Hu said: “It is not right for the offering of the sinner to mix with the offering of the righteous, therefore it was prohibited.” And this is what is stated here – Sarah Imeinu sought the prohibition of wool and flax so that the offering of the sinner would not mix, etc. Therefore, one must separate between Yitzchak and Yishmael the wicked, and thus she said to banish Hagar and Yishmael so that her righteous son will not learn from his evil ways.
