ריש רבא בשכר שאמר אברהם אבינו ואנכי עפר ואפר זכו בניו לב' מצות אפר פרה ועפר סוטה (Sota 17a)
What is the midah k'neged midah here? Why should the parsha of sota be the reward for Avraham expressing his humility and saying that he is like dust? The same question of course applies to the reward of the ashes of parah adumah for Avraham saying he is like ash. What's the connection?
When I was discussing this with my wife during the week she suggested that in order for the water of sotah to work, Hashem's name, which was written on the megilas sota, is dissolved and erased in the water. Chazal explain that Hashem is mochel on his kavod, so to speak, and allows his name to be erased in order to make peace between husband and wife. Because Avraham behaved with humility and did not stand on his honor, Hashem in turn does not stand on his honor when it comes to our sake. Baruch she'kivant, the Lubavitcher Rebbe says exactly this same idea.
The Rebbe further explains that ashes of parah adumah are metamei the person who engages in their preparation. The humility of Avraham Avinu ingrained in our genes is what allows a person to not stand on their honor and to become tamei in order to go out and bring tahara to a fellow Jew. A beautiful idea that perfectly fits the Rebbe's outlook.
The L Rebbe's focus is on the preparation of the mei sotah, the preparation of the mei chatas. Shem m'Shmuel focusses on the person who is tamei and needs the mei chatas to become tahor. Unlike other korbanos that are offered in the mikdash, the parah adumah is burned outside the machaneh. Just like a person who offers a korban is supposed to envision what is done to the animal as if it was done to their person (Ramban beginning of VaYikra), so too, a person who is tamei should envision himself as outside the camp, apart from the sanctified and pure community of klal yisrael, just like the parah. The burning of the parah to ash and the use of the lowly eizov plant serves to emphasize the individual's debasement. How does a person summon up the resolve to undergo such a process? Shem' m'Shmuel (Ki Tisa 5678) explains that it comes from the legacy we inherit from Avraham:
וי"ל שגם ההכנעה גופא זיכה אאע"ה לבניו שבאמת איננו דבר נקל לאדם לראות א"ע באמת כאלו הוא עומד חוץ לשלשה מחנות ולהשפיל עצמו כאזוב ותולעת כברש"י, אלא זכותו של אאע"ה שאמר אנכי עפר ואפר הכניס טבע זו בזרעו אחריו שיהי' ביכולתם להשפיל א"ע ולהיות באמת כעפר ואפר ואזוב ותולעת:
I would say the same is true of sotah. Chazal explain that the sotah ritual was a public spectacle which other women were invited to come and observe. The strength to undergo the public humiliation involved in the sotah process comes from Avraham Avinu. It's built into our nature.
If we read the gemara carefully, it is not parah in general, or sotah in general, that Avraham is rewarded with, but it's specifically the dust used for the sota water and the ashes of the parah. Sefas Emes (5650) reminds us that man was created from dust - עָפָר֙ מִן־הָ֣אֲדָמָ֔ה (Braishis 2:7), and in fact, all of creation is rooted in dust - הַכֹּל֙ הָיָ֣ה מִן־הֶֽעָפָ֔ר וְהַכֹּ֖ל שָׁ֥ב אֶל־הֶעָפָֽר (Koheles 3:20). Rashi in Braishis explains that it was not just any dust that was used in the creation of man, but it was the dust from the mikdash: דבר אחר: נטל עפר שלוב ממקום שנאמר בו: מזבח אדמה תעשה לי (שמות כ׳:כ׳), הלואי תהיה לו כפרה ויוכל לעמוד. When a person says "nafshi k'afar ti'hiyeh," it's this afar that is being referred to. It means returning to your roots, to the essence of who you are and what you are about. Are you living a life of luxury, or do you define yourself as מזבח אדמה תעשה לי, living a life of sacrifice for Hashem? In a few weeks we will read Balak's words מִ֤י מָנָה֙ עֲפַ֣ר יַעֲקֹ֔ב. What people other than us have such a legacy of afar? Chazal tell us in Pirkei Avos הוי מתאבק בעפר רגליהם. When we speak of Chazal, even the regel, the lowest level of a person, is afar ha'mikdash. That is the legacy of Avraham Avinu.
Chazal tell us that if the sotah is innocent, she will have a child. Shem m'Shmuel asks how this works. The sotah water is like poison. If the woman is guilty, she drinks it and explodes. How can the same water be the source of bracha? He quotes a similar question from the Zohar: kohanim are a source of bracha. We have birkas kohanim in our parsha. How then can the kohen be the instrument by which the sotah ritual is performed? The answer is that the water itself in neither inherently good or bad. It just serves as the catalyst to bring out the person's core. If the person's "lifestyle" is incompatible with afar that is from מזבח אדמה תעשה לי, then the woman will explode. But if the person's identity is in concert with the afar of Avraham Avinu, then the same water can be a source of bracha.
I want to suggest one additional approach to the relationship between the parsha of sotah and Avraham's great humility of "afar v'eifer" based on R' Tzadok haKohen's analysis (Pri Tzadik Naso section 3 and 6) of the structure of our parsha. The book of Bamidbar began with the layout of the shevatim around the mishkan and then spoke about the levi''im and their tasks in the mishkan. You would expect the parsha to jump right to the gifts of the nesi'im brought to celebrate the inauguration of the mishkan. Why are the parshiyos of gezel ha'ger, sotah, and nazir stuck in the middle here? Ralbag (see Abarbanel as well) writes that the arrangement of the camp of Bnei Yisrael was set out to create harmony between the shevatim. Everyone has a place and knows where they belong. Gezel ha'ger addresses the issue of crime, which would inevitable ruin the harmony achieved. להסיר הרע מן המחנה אשר יביא למריבה וקטטה; והוא, שיהיה האדם נזהר מלהחזיק בממון חבירו שלא כדין. Sotah drills down further and ensures harmony of the home. Finally, the parsha of nazir comes to create harmony within the psyche of the individual himself, to curb the tension between lust for wine and pleasure and the pursuit of a more spiritual life. R' Tzadok haKohen has a different approach. Without getting into the details, he sees the structure of the parsha as addressing the kedusha of the individual, which is a microcosm of the kedusha of the klal. Setting up a harmonious camp where everyone has a place and every tribe knows their role is worthless if on an individual level a person feels spiritually lost and not rooted. Life is filled with challenges and complications and we all mess up from time to time, so how do you keep that sense of knowing that you belong, or where you belong? The parsha therefore introduces gezel ha'ger and the concept of וְהִתְוַדּ֗וּ אֶֽת־חַטָּאתָם֮ אֲשֶׁ֣ר עָשׂוּ֒ which is the basis of the mitzvah of teshuvah. If you make a mistake, you can repent. The theme of sotah, says R' Tzadok, is not shalom bayis, bur rather וְנֶעְלַם֙ מֵעֵינֵ֣י אִישָׁ֔הּ. You can repent only if you know what you did wrong, but there are the wrongs that we are unaware of, things outside our mental line of vision. Parshas sotah tells us that Hashem can bring us birur even for those things. Finally, there is the parsha of nazir, the person who aims for an even higher state of perfection.
The difference between a humble person, a person who sees themselves as "afar v'eifer," and a person who is full of themselves, I think is this quality of וְנֶעְלַם֙ מֵעֵינֵ֣י אִישָׁ֔הּ, of accepting that there are things outside your knowledge, outside your control. Avraham prayed for Sdom, but it was done with an acknowledgment that he was doing so despite being וְאָנֹכִ֖י עָפָ֥ר וָאֵֽפֶר, despite perhaps lacking the full picture, a picture that only G-d can see. What may seem unjust may be due only to our limited vision. Hashem therefore midah k'neged midah promised Avraham in reward for that acknowledgment that He will help with the tikun needed even for those areas.
If you think you know it all and see it all, then Hashem will not interfere and will allow you to make your own way and the chips can fall where they may. But if you acknowledge that you can't really do it alone, then He is there to help get you beyond your blindspots.