There are three reasons why this makes sense. First, the statistics correlate almost perfectly. Second, it holds true worldwide with no exceptions. Every country studied has shown this same strong correlation between leaded gasoline and violent crime rates. Third, the chemistry and neuroscience of lead gives us good reason to believe the connection. Decades of research has shown that lead poisoning causes significant and probably irreversible damage to the brain. Not only does lead degrade cognitive abilities and lower intelligence, it also degrades a person’s ability to make decisions by damaging areas of the brain responsible for emotional regulation, impulse control, attention, verbal reasoning, and mental flexibility.
Another thing that stands out: if you overlay a map showing areas with higher incidence of violent crime with one showing lead contamination, there's a strikingly high correlation.