When a star reaches the red giant phase, why does it become more opaque?
There are some answers in this lecture and this one although even there the author admits that the whole story is complicated, and not perfectly known. 

It seems that shell burning and contraction of the no-longer-burning core of the star causes some expansion of the outer layers (this is described as the "mirror principle" and partly explained in lecture 12 (section 12.4). This causes the outer layers to cool, until H- ions start to form in them (around 5000K). These interact with light much more than neutral hydrogen atoms or bare protons (H+) which accounts for the increase in opacity.