How can skull size difference alone explain behavioral differences using evolutionary theory?
Having a large difference between the sizes of the skulls between males and females is strong sign of sexual dimorphism, particularly of males that are larger in general.  Knowing which form of sexual dimorphism there is allows you to predict several other features. In particular large males is seen almost exclusively in animals in which the males fight each other for control of a harem AKA contest competition. This means high male aggression, since they are driving away other males. Since they drive away other males they have little to no sperm competition so they also don't need competitive sperm. These species also show drastic difference in male reproductive success, males with a harem produce many offspring males without one produce few to none. 

https://www.intechopen.com/books/sexual-dimorphism/the-evolution-of-sexual-dimorphism-understanding-mechanisms-of-sexual-shape-differences