Why is economic profit for a monopoly per unit demand minus ATC? I understand that the P-ATC gives the per unit economic profit 

Why is this the case? Why wouldn't we take price minus the marginal cost?
Price minus marginal cost gives you marginal profit.

\begin{align*}
\text{Total profit}&amp;=\text{Revenue}-\text{Total cost}\\
\frac{\text{Total profit}}{\text{Quantity}}&amp;=\frac{\text{Revenue}-\text{Total cost}}{{\text{Quantity}}}\\
&amp;=\frac{\text{Revenue}}{{\text{Quantity}}} - \frac{\text{Total cost}}{{\text{Quantity}}}\\\\
\text{Per-unit profit}&amp;=\text{Price}-\text{Average total cost}
\end{align*}