The Medrash (Yalkut Shimoni Mishlei 959) states: “With this Aharon will come...with the zechus of the milah.”
Sefer Har Besamim explains by quoting a Medrash (cited in Bnei Yissochor, Chodesh Tishrei, Maamar 4, Ois 7) that says that when Hashem made Eliyahu the “Malach Habris”, Eliyahu said, “Ribono Shel Olam. You know that my middah is to zealously avenge You. If I come to a bris and the father of the baby is a sinner, I won’t be able to hold myself back from taking action against him. Wouldn’t it be better to choose for this task a different malach that does not possess this spirit of zealousness?”
Hashem told him, “In your merit, I will forgive the father of the baby on the day of the bris and there will be no need for you to avenge Me.”
Eliyahu then said, “But what if the mohel or sandak or one of the guests is a sinner? I won’t be able to hold myself back from harming them.”
Hashem then said, “Anyone who attends a bris will have their sins forgiven!”
Eliyahu then calmed down and accepted the task of attending every bris. We see from this that anyone who attends a bris has all of their sins forgiven.
The reason Aharon entered the Kodesh was to provide atonement for Yidden who needed to have their sins forgiven, as is stated: “And he will atone for himself and for his household and for all of the assemblage of Yisroel.” Thus, when we go to a bris milah, we can accomplish what Aharon accomplished by entering the Kodesh. Accordingly, the Medrash’s intent is that Aharon entering the Kodesh and the zechus of bris milah serve the same purpose.
