canonical height of elliptic curve has property $h(P+Q)+h(P-Q)=2h(P)+2h(Q)$. Is there any reason to expect it?

Question

Let $E(Q)$ be an elliptic curve over $Q$. Let $h(P)$ be canonical height.

Then $\forall P,Q\in E(Q)$, $h(P-Q)+h(P+Q)=2h(P)+2h(Q)$.

$\textbf{Q:}$ Is there any reason to expect structure $h(P-Q)+h(P+Q)=2h(P)+2h(Q)$? This looks like parallelogram law without squaring.

Ref. Knapp Elliptic Curves Prop 4.14 of Chpt 4, Sec 5.