You clearly approached this article with preconceived ideas about a high-fat diet, and you let that affect the advice you gave to people who may or may not see you as an expert. The evidence relating to high-fat diets and testosterone levels that you cited clearly shows a positive relationship between high-fat/low-carb diets and boosting testosterone levels. Not only that, but the study you referenced, when providing ‘evidence’ for high carb diets being beneficial in improving testosterone levels in the body, is irrelevant as it is not statistically significant with a total sample size of 20. Yet you still decide to go against the evidence and recommend to your readers that they should stick to a high-carb diet.
The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.     
Testosterone patches are effective at treating low libido in post-menopausal women. Low libido may also occur as a symptom or outcome of hormonal contraceptive use. Women may also use testosterone therapies to treat or prevent loss of bone density, muscle mass and to treat certain kinds of depression and low energy state. Women on testosterone therapies may experience an increase in weight without an increase in body fat due to changes in bone and muscle density. Most undesired effects of testosterone therapy in women may be controlled by hair-reduction strategies, acne prevention, etc. There is a theoretical risk that testosterone therapy may increase the risk of breast or gynaecological cancers, and further research is needed to define any such risks more clearly.