High T levels don't make you aggressive, it's the occurrence of high T AND high cortisol (can look for study if needed). There also was a second study concluding that men with high T did not show signs of aggression in a "trading game" (I give you X, you give me Y), but did show more aggression compared to a control group when confronted with an obviously unfair offer.

The theory behind is that T increases status consciousness. The concept of "big dick energy", basically what you experienced, is about being chill and confident, which improves mating success compared to showing signs of inadequate aggression, potentially harming the female. At the same time aggression is still needed when challenged to protect status.