What is the difference between "spontaneous" and "energetically favourable"?
Here is a very simple example of an exothermic, nonspontaneous process at room temperature:

$$\ce{H2O_{(l)} -&gt; H2O_{(s)}}$$

You need to extract heat from water to freeze it, but it is obvious that at $25\ ^{\circ}\mathrm{C}$, this does not happen spontaneously. Only if you decrease the temperature to decrease the contribution of the negative $\Delta S$ term will this reaction occur spontaneously.