In Atkins' Physical Chemistry the criteria for spontaneity using Gibbs energy was calculated using the Clausius inequality:
$$\mathrm dS ≥ \frac{\mathrm dq}{T},$$
and at constant pressure, $\mathrm dq = \mathrm dH.$ Thus, $\mathrm dH - T\,\mathrm dS$ is negative.
So, if we define a function $G = H - TS$ at constant pressure and temperature, we get
$$\mathrm dG = \mathrm dH - T\,\mathrm dS ≤ 0,$$
which we use as a criteria for spontaneity.
My issue with this argument is that it implies that the Clausius inequality is for spontaneous processes only, otherwise we would end up with $\mathrm dG ≤ 0$ for all processes.
However, the derivation of the inequality simply used the fact that
$$|\mathrm dW_\mathrm{reversible}| > |\mathrm dW_\mathrm{irreversible}|$$
when the system does work.
So, where is it implied that the derivation is for spontaneous processes only?