Of the several ways to derive the evidence lower bound (such as using Jensen’s inequality), a version often used is the derivation from $KLD(q(z) || p(z|x))$.
The following image illustrates the derivation process (screenshotted from here):
While I do understand how the math works out, I do not have an argument for using $KLD(q(z) || p(z|x))$ as a starting point. Why $KLD(q(z) || p(z|x))$, and not $KLD(q(z) || p(z))$ or $KLD(q(z|x) || p(z|x))$?
If someone asks me the motivation of wanting to calculate $KLD(q(z) || p(z|x))$ (as opposed to KLD between other distributions, as listed above), what can I tell them?