Parah adumah awakens inherited humility

בטעם עץ ארז כו' ישפיל עצמו ויתכפר לו.

Regarding the reason for the cedar wood, etc. [in the parah adumah]: let him lower himself, and he will be atoned for.

The Sefas Emes cites the Midrashic teaching that the tall cedar used in the parah adumah hints that a person must humble himself - lower his lofty self-regard - in order to attain atonement.

הגם כי אין ניכר בהזאה ענין הרמז שבשעת שריפת הפרה.

Although the matter of the allusion present at the time of the burning of the cow is not evident in the sprinkling [of the ashes].

He concedes a difficulty: the symbolism of humility is bound up with the original burning of the parah, yet the act of sprinkling the ashes upon the impure person does not visibly reflect that lesson.

מ"מ בכל מצוה יש ענין מיוחד מסוגלת במצוה זו.

Nevertheless, in every mitzvah there is a special quality uniquely suited to that mitzvah.

Each mitzvah carries its own particular spiritual power, a segulah inherent specifically to it.

כמו כן הזאת פרה מביא הכנעה לאדם.

So too, the sprinkling of the parah brings humility (hachna'ah) to a person.

Even the sprinkling itself carries the segulah of the parah adumah - it instills submission and self-humbling in the person being purified.

ואיתא בשכר שאמר אברהם אנכי עפר ואפר ניתן אפר פרה לבניו.

And it is taught: in reward for Avraham having said, "I am but dust and ashes" (Bereishis 18:27), the ashes of the parah were given to his children.

Avraham Avinu's profound humility - calling himself mere "dust and ashes" - earned his descendants the purifying ashes of the parah adumah.

והענין כנ"ל שמרוב הכנעה רבה שהי' באברהם אע"ה זכו בניו אחריו להיות כל איש ישראל בכחו להכניע עצמו ע"י מצות אפר פרה.

And the matter is as above: from the abundance of great humility that was in Avraham Avinu, his children after him merited that every member of Yisrael has within his power to humble himself through the mitzvah of the ashes of the parah.

Avraham's vast humility was implanted as a permanent capacity in his descendants. Through the mitzvah of the parah's ashes, every Yid can draw on that inherited power to bring himself to genuine hachna'ah.

והנה גם עתה ע"י קריאת הפרשה מתעורר הכנעה וביטול זה בלבות בני ישראל:

And behold, even now, through the reading of the parsha, this humility and bittul is awakened in the hearts of Bnei Yisrael.

Even today, without the actual ashes, the very reading of Parshas Parah arouses that same inherited power of hachna'ah and bittul within the hearts of Bnei Yisrael.

Summary: The cedar of the parah adumah teaches that humility brings atonement, and though that lesson is tied to the burning of the cow, every mitzvah carries its own unique segulah - here, the power to instill hachna'ah. In reward for Avraham's "I am dust and ashes," his descendants received the parah's ashes, embedding in every Yid the inherited capacity to humble himself. Even now, the mere reading of Parshas Parah awakens that humility and bittul in the hearts of Bnei Yisrael.