For me, the strongest argument in favor of evolutionary psychology is how well it works for explaining social behaviours of non-human animals. I think this is important background material to understand where evolutionary psychologists come from. I recommend parsing through the following textbooks:

Animal Behaviour, Alcock

An Introduction to Behavioural Ecology, Krebs and Davies

(Disclaimer: I have only read Alcock, but Krebs and Davies is supposed to be stronger and better organized from a theoretical point of view - Alcock has wonderful examples.)

Of course, human social behaviour is orders of magnitude more diverse and complicated than in any other species - and even for other primates, one already needs to adopt the point of view of sociology and social psychology to get a good picture. But the premise that culture somehow freed us from all this background of behavioural adaptations is very strange, especially given the tendancy of the evolutionary process to recycle everything in sight into new shapes and patterns.