Teshuvah Turns Sins into Inadvertent Ones

בפסוק לטהר אתכם מכל חטאתיכם וחטא הוא שוגג לכן אמרו חז"ל דיוהכ"פ בעי תשובה.

On the verse "to purify you from all your sins" - and "cheit" denotes an unintentional sin (shogeg); therefore Chazal said that Yom Kippur requires teshuvah.

The verse (Vayikra 16:30) speaks of being purified from "chataeichem." Since the word "cheit" specifically connotes inadvertent sin, while Yom Kippur is meant to atone even for deliberate sins, Chazal taught that one must do teshuvah for the day to atone fully.

וע"י התשובה גם מיראה הזדונות נעשין שגגות ואז היוהכ"פ מכפר על השגגות.

And through teshuvah - even teshuvah out of fear (yirah) - deliberate sins (zedonos) become as unintentional ones (shegagos), and then Yom Kippur atones for the unintentional sins.

Teshuvah me'yirah (repentance motivated by fear of Hashem) has the power to downgrade willful sins into the category of inadvertent ones. Once that transformation happens, the day of Yom Kippur itself can do its work, since it atones for the level of "shegagos."

וזהו שאומרים כי לכל העם בשגגה שעכ"פ כולם עושין תשובה עכ"פ מיראה:

And this is what we say, "for all the people sinned unintentionally (bi-shgagah)" - that at the very least everyone does teshuvah, at least out of fear.

In the Yom Kippur davening we declare that the whole nation sinned "bi-shgagah." How can we say that of everyone? Because at minimum every Jew does teshuvah me'yirah, which converts even his willful sins into inadvertent ones - so it is true that, in effect, all the people stand in the category of shogeg, and the day atones for them.

Summary: Since the Torah speaks of purification from "cheit" (inadvertent sin), Yom Kippur on its own atones only for unintentional sins. Teshuvah - even teshuvah me'yirah (out of fear) - has the power to recategorize deliberate sins as inadvertent ones, so that the day can then atone for them. This is why we can declare that "all the people sinned bi-shgagah": through their teshuvah me'yirah, the whole nation is placed in the category of shogeg.