There are no inconsistencies here. We have an algebraic indentity, a + b = x + y. (Let's not even think about what those might represent; it doesn't matter.)

There are no inconsistencies here. We have an algebraic indentity, a + b = x + y. (Let's not even think about what those might represent; it doesn't matter.) The two sides must always be equal. Any transaction must maintain that equality. Therefore, any transaction must increase both sides by the same amount, decrease both sides by the same amount, or leave both sides unchanged. One way to ensure this is respected is to add up everything which increases the left side or decreases the right side, then add up everything which decreases the left side or increases the right side, and ensure these two subtotals match. If they do, the transaction balances, and is legal. By convention, we call things of the first type (which increase the left side or decrease the right side) "debits", and things of the second type (which increase the right side or decrease the left side) "credits". This lets us say "debits must equal credits" as a shorthand, although again what we really mean is that the two sides must continue to balance. The end. There's really no inconsistency here.