On Yom Kippur we confess to sins we did not commit (as well as a bunch we did commit).
One explanation is that we do not only speak individually, but also confess as Clal Yisrael, the entire people Israel. Another is that the confession is intended to remind us how many impulses, ideas — how many selves — we truly are.
The conduct of biblical heroes — David in particular, but others as well — highlights the inconsistency of personality. The same individual can be heroic one minute and craven the next. We experience this when watching a movie or reading a book; now we identify with the hero, now the villain, now the bystander. The great Polish poet Czeslaw Milosz wrote that the purpose of poetry is to remind us how hard it is to remain just one person.
We cohere in some loose way, of course. But it is a salutary reminder: in judging the limitations of others remember how often you can be a stranger to yourself. Moses did not know that he harbored a hero until God called him; we are both slight sparks and inexhaustible images of the One who contains all.