Negative number represent the "absence" of something, at least in cases like this. So, owing someone 1$ is like having -1$.
In fact, suppose that you receive 10$. Since you had a debt of 1$, you actually have 10-1=9$.
So, debits are represented by negative numbers, and credits are represented by positive numbers.
By definition, negative numbers are smaller than zero, and thus they are located left of zero on the number line.