Yom Kippur Bris

In Pirkay D'rebbe Eliezer (Ch. 29) it says that the milah of Avraham took place on Yom Kippur, אתיא "עצם" מ"עצם" מיום הכפורים, מה להלן (ויקרא כג, כח): "כָּל מְלָאכָה לֹא תַעֲשׂוּ בְּעֶצֶם הַיּוֹם הַזֶּה כִּי יוֹם כִּפּוּרִים הוּא", שביום הכפורים נמול אברהם, ובכל שנה ושנה הקב"ה רואה דם הברית של מילה של אברהם אבינו, ומכפר על כל עונותינו, שנאמר (ויקרא טז, ל): "כִּי בַיּוֹם הַזֶּה יְכַפֵּר עֲלֵיכֶם לְטַהֵר אֶתְכֶם".   Why did the bris of Avraham take place on Yom Kippur? And how does that atone for us?  

The possuk in Tehillim (139:16) says יָמִ֥ים יֻצָּ֑רוּ ולא (וְל֖וֹ) אֶחָ֣ד בָּהֶֽם.  Chazal say the one day designated to Hashem, the לו אחד is Yom Kippur.  The קרי of the possuk is לא, to say Hashem is not just is one of the days.  This means that on Yom Kippur it is revealed that it is a day designated for Hashem.  However, that is not merely to be on Yom Kippur but is meant to affect the rest of the days of the year as well.  ועניתם את נפשתיכם בתשעה לחדש בערב מערב עד ערב תשבתו שבתכם.  Chazal ask but we don't fast on the ninth day, we fast on the tenth?  The derash is one who eats on the ninth and fasts on the tenth is as if he fasted both days.  The same can be extended for the next words, עד ערב, the fast is in the day, not in the evening?  If one eats at night, if one takes the joy of Yom Kippur and extends it into the year, its as if one fasted then as well.  The radiance and kedusha of Yom Kippur extends throughout the year if one appreciates its atonement. 

The ערלה represents that which is tumah, klipah, external to one's spiritual growth.  The commandment of milah is reveal one's essence of kedusha.  That is why the limud to tell us that Avroham's bris took place on Yom Kippur is in the words בעצם היום, because it is the עצמיות, the essence of a person, when all the outside factors are removed, that becomes revealed.  That is why the דם ברית of Avraham is what gives us the merit of atonement.  Avraham's bris was not just for himself but his middot became part of his very makeup and were passed down through the genes as described in Tanya Ch. 18-19.  Hashem looks at the essence of a Jew, when the foreskin is removed an sees the pure soul.  Just as the radiance of Yom Kippur can be extended into the year, so too one's kedusha of the bris milah can elevate all the limbs of a person (based on Sfas Emes Yom Kippur 5652.)