Why does a star of
average mass expand
into a red giant?

When a star expands, the surface of the star becomes cooler as well as redder. Hence, forming the red giant.

Explanation:

If all the hydrogen which is present in a star gets fused into helium then an increase in the core temperature can be seen along with the core contractions. As a result of these core pressures and the core temperatures, the helium gets fused into carbon through a process known as the triple alpha process. As a result, the star begins to expand whereas its surface becomes cooler and redder which leads to the formation of red giant.