There is a pretty good talk by Robert Sapolsky on the subject, and as a researcher he did a meta study in the subject. If you want to fast forward, 30:15 is a good place to start.

https://youtu.be/2bnSY4L3V8s?t=1815

To summarize in text, Testosterone does not cause aggression. It amplify existing defensive behavior in the context of a persons social status being challenged. A person that has high status, or more significantly gains social status, also trigger higher levels of Testosterone. In turn Testosterone increases behavior which in the cultural context maintain that new won status.