The passage explains that the red heifer purifies the impure and makes the pure impure because opposites affect each other while things of the same kind do not; since water is pure purity and the heifer's ash is pure impurity mixed together, the pure water in the sprinkling water overcomes and purifies an impure person (who is not affected by the ash since both are impure), while that same water makes a pure person impure (being opposite to them).
וּמַזֵּה מֵי הַנִּדָּה יְכַבֵּס בְּגָדָיו. רֹב הַמְפָרְשִׁים יָצְאוּ לְלַקֵּט וְלֹא מָצְאוּ טַעַם מַסְפִּיק לָמָּה הַפָּרָה הַמְטַהֶרֶת הַטְּמֵאִים תְּטַמֵּא הַטְּהוֹרִים. וְעַתָּה הַט אָזְנְךָ וּשְׁמַע, כִּי מָצִינוּ שֶׁכָּל אֹכֶל אֵינוֹ מֻכְשָׁר לְטֻמְאָה עַד שֶׁיִּפּוֹל עָלָיו מַיִם. וְאֵיךְ אֶפְשָׁר הַמַּיִם שֶׁמְּקוֹרָם טָהֳרָה יְסַבְּבוּ הַטֻּמְאָה? אֶלָּא בֵּאוּר הָעִנְיָן כָּךְ הוּא: שֶׁכָּךְ הוּא בַּטִּבְעִיּוֹת, שֶׁכָּל דָּבָר אֵינוֹ מִתְפָּעֵל כִּי אִם מֵהַפְכּוֹ, וְלֹא מִמָּה שֶׁהוּא מִמִּינוֹ. כְּדֶרֶךְ שֶׁהַיֵּצֶר הָרָע מִתְגָּרֶה יוֹתֵר בְּיִשְׂרָאֵל מִבָּאֻמּוֹת, וּבְתַלְמִידֵי חֲכָמִים יוֹתֵר מִכֻּלָּם (סוכה נב.), לְפִי שֶׁכֻּלָּם הַפְכִּיִּים לוֹ, עַל כֵּן הוּא רוֹצֶה לְהִתְגַּבֵּר עֲלֵיהֶם. וְזֶה טַעַם שֶׁסָּמוּךְ לַעֲלִיַּת הַשַּׁחַר הַחֹשֶׁךְ מִתְגַּבֵּר, כִּי כָּל דָּבָר מִתְפָּעֵל מֵהַפְכּוֹ דַּוְקָא. לְפִיכָךְ, כָּל אֹכֶל וְזֶרַע אֵינוֹ מִתְפָּעֵל מִן הַטֻּמְאָה לַעֲשׂוֹת בּוֹ רוֹשֶׁם עַד שֶׁיָּבֹא עָלָיו מַיִם שֶׁכֻּלָּם טָהֳרָה, וְאָז הַטֻּמְאָה רְצוֹנָהּ לְנַצֵּחַ הַטָּהֳרָה וּמִתְגַּבֵּר עָלֶיהָ וְעוֹשֶׂה בָּהּ רוֹשֶׁם. כָּךְ מֵי נִדָּה שֶׁיֵּשׁ בָּהֶם מַיִם שֶׁכֻּלָּם טָהֳרָה, וְיֵשׁ שָׁם אֵפֶר פָּרָה שֶׁכֻּלּוֹ טֻמְאָה, וְהֵם מְעֹרָבִין יַחַד. לְפִיכָךְ, אִם מֵי נִדָּה זוֹרַק עַל אָדָם טָמֵא, אָז אֵין הָאָדָם מִתְפָּעֵל מִן הָאֵפֶר, שֶׁהֲרֵי הוּא מִמִּינוֹ, אֲבָל הוּא מִתְפָּעֵל מִן הַמַּיִם שֶׁהֵם הַפְכִּיִּים לוֹ, כִּי הוּא טָמֵא וְהַמַּיִם טְהוֹרִים, עַל כֵּן הַמַּיִם פּוֹעֲלִים בּוֹ וּמְנַצְּחִים הַטֻּמְאָה. אֲבָל אָדָם טָהוֹר הַנּוֹשֵׂא מֵי הַנִּדָּה אֵינוֹ מִתְפָּעֵל מִן הַמַּיִם, כִּי הֵם מִמִּינוֹ, שֶׁשְּׁנֵיהֶם טְהוֹרִים. אֲבָל הוּא מִתְפָּעֵל מִן הָאֵפֶר שֶׁהֵם הַפְכִּיִּים לוֹ, כִּי הוּא טָהוֹר וְהָאֵפֶר טָמֵא, עַל כֵּן הָאֵפֶר פּוֹעֵל בּוֹ וְעוֹשֶׂה בּוֹ רוֹשֶׁם לְטַמְּאוֹ. וְעַל צַד הָרֶמֶז מָקוֹם אִתִּי לוֹמַר עַל פִּי דִּבְרֵי בַּעַל הָעֲקֵדָה, שֶׁפֵּרֵשׁ כָּל עִנְיְנֵי הַפָּרָה עַל דַּרְכֵי הַתְּשׁוּבָה, כַּמְבֹאָר מִסִּפְרוֹ. וְעַל זֶה הַדֶּרֶךְ קָרוֹב לִשְׁמֹעַ, שֶׁרְפוּאַת הַנֶּפֶשׁ כִּרְפוּאַת הַגּוּף, כִּי הַמַּשְׁקֶה הַמּוֹעִיל לִתְרוּפַת אָדָם חוֹלֶה מַזִּיק לְאָדָם בָּרִיא. וּכְאָמְרוּ רַזַ״ל (תענית יא:): בַּר בֵּי רַב דְּיָתֵיב בְּתַעֲנִיתָא, כַּלְבָּא לֵיכוֹל שֵׁירוּתָא. הֲרֵי שֶׁהַצּוֹמוֹת מְטַמְּאִים אֶת הַטְּהוֹרִים וּמְטַהֲרִים הַטְּמֵאִים. פֵּרוּשׁ: מִי שֶׁנִּטְמָא כְּבָר בַּעֲבֵרָה, הַצּוֹמוֹת הֶכְרֵחִיִּים לוֹ, וּכְהַהִיא שֶׁאָמְרוּ רַזַ״ל (יומא פו:): הֵיכִי דָּמֵי בַּעַל תְּשׁוּבָה? כְּגוֹן שֶׁבָּא אוֹתוֹ מַעֲשֶׂה לְיָדוֹ וּפֵרַשׁ מִמֶּנּוּ. מַחְוֵי רַב יְהוּדָה: בְּאוֹתוֹ פֶּרֶק וּבְאוֹתָהּ אִשָּׁה וּבְאוֹתוֹ מָקוֹם. כִּי מְקוֹם הַחֵטְא וְשַׁעַר שֶׁעָבַר בּוֹ צָרִיךְ שֶׁשָּׁם תִּהְיֶה גְּבוּרָתוֹ לְהִתְגַּבֵּר עַל יִצְרוֹ, שֶׁכְּבָר טָעַם פֹּה טַעַם עֲבֵרָה וּמְבַקֵּשׁ לִמּוּדוֹ. וְזֶהוּ שֶׁכָּתוּב (הושע ב א): ״וְהָיָה בִמְקוֹם אֲשֶׁר יֵאָמֵר לָהֶם לֹא עַמִּי אַתֶּם, יֵאָמֵר לָהֶם בְּנֵי אֵל חָי״, דַּוְקָא בִּמְקוֹם הַחֵטְא, אֲשֶׁר שָׁם יֵאָמֵר לָהֶם לֹא עַמִּי אַתֶּם, בַּמָּקוֹם הַהוּא תִּהְיֶה הַתְּשׁוּבָה, וְשָׁם יֵאָמֵר לָהֶם בְּנֵי אֵל חָי.
And he who sprinkles the water of sprinkling shall wash his clothes. Most commentators have gone out to gather [explanations] but have not found a sufficient reason why the [red] heifer, which purifies the impure, would make the pure impure. Now, incline your ear and listen, for we find that no food is susceptible to impurity until water falls upon it. How is it possible that water, whose source is purity, would cause impurity? Rather, the explanation of the matter is as follows: It is natural that everything is only affected by its opposite, not by what is of its own kind. This is similar to how the evil inclination provokes Israel more than the nations, and Torah scholars more than anyone else (Sukkah 52a), because they are all opposite to it, therefore it wants to overcome them. This is the reason why darkness intensifies just before dawn, because everything is affected specifically by its opposite. Therefore, no food or seed is affected by impurity to make an impression until water, which is all purity, comes upon it. Then the impurity wants to defeat the purity, overcomes it, and makes an impression on it. Similarly, the water of sprinkling contains water which is all purity, and the ashes of the [red] heifer which is all impurity, and they are mixed together. Therefore, if the water of sprinkling is thrown on an impure person, the person is not affected by the ash because it is of his kind [both being impure], but he is affected by the water which is opposite to him, because he is impure and the water is pure. Therefore, the water acts upon him and overcomes the impurity. But a pure person who carries the water of sprinkling is not affected by the water because it is of his kind, as both are pure, but he is affected by the ash which is opposite to him, because he is pure and the ash is impure. Therefore, the ash acts upon him and makes an impression to make him impure. And by way of allusion, I have a place to [explain it], based on the words of the author of the Akedah, who interpreted all matters of the red heifer as representing the ways of repentance, as explained in his book. Along this approach, it is reasonable to understand that the healing of the soul is like the healing of the body, for a medicinal drink that benefits a sick person can harm a healthy person. As our Sages said (Taanit 11b): “A scholar who sits in fasting, a dog should eat his meal.” This shows that fasts defile the pure and purify the defiled. Meaning, for one who has already been defiled by sin, fasts are necessary for him, as in the statement our Sages made (Yoma 86b): “What constitutes a true penitent? One who encounters the same situation where he sinned, and abstains.” Rabbi Yehudah explained: “With the same woman, at the same time, and in the same place.” For at the place of sin and the gate through which one transgressed, there must be his strength to overcome his evil inclination that has already tasted the flavor of sin there and seeks to repeat it. This is what is meant by the verse: And it shall be, in the place where it was said to them, ‘You are not My people,’ it shall be said to them, ‘You are the children of the living God’ (Hosea 2:1). Specifically in the place of sin, where it was said to them, You are not My people, in that very place will be the repentance, and there it will be said to them, You are the children of the living God.