Veltz,
When a person commits themselves to adhering to the halacha in certain areas and finds that he becomes a better person as to those areas it strengthens his emunah that the Torah system works and by extension is more likely to be divine.
So if a person finds he has anger issues and suppresses his anger in various situations in an attempt to follow the halacha and mussar, and then over the course of time finds that he no longer gets angry altogether, he concludes that he has fixed (to a degree at least) a character trait through Torah.