"Rabbi Eliezer ben [son of] Yaakov said, 'One who fulfills one mitzvah acquires himself a single defending angel. One who commits one transgression acquires one accusing angel. Repentance and good deeds serve as a shield before retribution'" (Avos 4:11).
So, according to the simple reading of this Mishna, if a person spends a lifetime doing mitzvos and does one sin, the mitzvos don't cancel out the sin. The sin is always there.
And the opposite is true. If a person spends a lifetime sinning, and does one mitzvah, those sins do not cancel out the mitzvah.
However, the Yalkutei HaGershuni asks, There is a concept of nullification in the Torah. Fifty-one percent nullifies forty-nine percent. And there is also a concept of nullification in Rabbinic law. One out of sixty in most cases, and in very specific cases, one out of a hundred and one out of two hundred.
For example, if a piece of meat fell into a pot of boiling milk. If the milk is sixty times larger than the piece of meat, you can remove the meat, and the milk will be completely kosher.
So, why is there no nullification regarding sins? Why can't one thousand mitzvos nullify one?
The Yalkutei HaGershuni answers, because that one sin is a "davar sh'yesih lo matirim," and there is no nullification for that.
What exactly does this mean? Something which is forbidden now, but will be allowed at a later time, is called a "davar sh'yesih lo matirim". For example. One piece of bread on Pesach (kosher, but owned by a non-Jew). On Pesach itself, it's obviously forbidden to eat. Yet, right after Pesach (since it was owned by a non-Jew), that piece of bread will be allowed. Therefore, if a piece of bread fell into soup on Pesach, even if the soup is one-thousand times the size of the piece of bread, there is no nullification and the entire soup is forbidden.
This sin, which is obviously forbidden, has an internal power to turn into "a shield before retribution" through proper tshuva.
Therefore, on one hand, this sin cannot be nullified. It will always be with you. However, you have the ability to take that sin and turn it into a spiritual shield. We have no need to nullify anything! We "simply" need to transform those sins into positive spiritual tools!
Have a wonderful Shabbos!