I suspect the answer is two-fold: First, the gel of Testim is alcohol based, and ANY alcohol on the scrotum or penis will BURN. Second, the application may be on the shoulders so that it will go immediately to the muscle mass most visible... but that is only a guess on my part. To tell the truth, I was going to ask the same question as you, but you beat me to it.
Also, the shoulders will be covered, avoiding contamination and those areas are most easily reached and rubbed, providing a concentration of the drug.
Plus, if you were in the men's locker room, you might more easily apply a gel to your shoulders without stares, than if you were rubbing your genitals, right?
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