Testosterone is significantly correlated with aggression and competitive behaviour and is directly facilitated by the latter. There are two theories on the role of testosterone in aggression and competition.  The first one is the challenge hypothesis which states that testosterone would increase during puberty thus facilitating reproductive and competitive behaviour which would include aggression.  Thus it is the challenge of competition among males of the species that facilitates aggression and violence.  Studies conducted have found direct correlation between testosterone and dominance especially among the most violent criminals in prison who had the highest testosterone levels.  The same research also found fathers (those outside competitive environments) had the lowest testosterone levels compared to other males. 
Another point I’d like to make for people worried about a link between high testosterone and prostate cancer is that it just doesn’t make sense. Prostate cancer becomes more prevalent in men as they age, and that’s also when their testosterone levels decline. We almost never see it in men in their peak testosterone years, in their 20s for instance. We know from autopsy studies that 8% of men in their 20s already have tiny prostate cancers, so if testosterone really made prostate cancer grow so rapidly — we used to talk about it like it was pouring gasoline on a fire — we should see some appreciable rate of prostate cancer in men in their 20s. We don’t. So, I’m no longer worried that giving testosterone to men will make their hidden cancer grow, because I’m convinced that it doesn’t happen.