Coca leaf is native to South America and grows best there, so that's where the cocaine comes from. Not only does this produce a huge amount of profit for organised crime, the drug itself promotes aggression. Almost all the drug wars are primarily concerned with cocaine and secondly with marijuana which also grows well there.
Colonialism, Communism and Coups
Latin America suffered brutality from Cortez onwards. Many of the smaller states had to fight wars of independence; Haiti was made to pay reparations to France for freeing its slaves, for example.
After World War 2, the US made a practice of opposing any government in the south that it considered too left wing. Frequently a democratically elected socialist government would be violently overthrown by CIA-backed forces and replaced with a dictatorship. See e.g. Guatemala from Wikipedia:
In 1954, the democratically elected Guatemalan government of Colonel Jacobo Arbenz Guzmán was toppled by U.S.-backed forces led by Colonel Carlos Castillo Armas who invaded from Honduras. Assigned by the Eisenhower administration, this military opposition was armed, trained and organized by the U.S. Central Intelligence Agency (see Operation PBSUCCESS). The directors of United Fruit Company (UFCO) had lobbied to convince the Truman and Eisenhower administrations that Colonel Arbenz intended to align Guatemala with the Soviet Bloc.
The resulting weak but brutal governments and ongoing wars with rebel groups have consumed many of the past decades. The war with FARC has been going on since 1964, for example. The Colombian right-wing militia are strong enough to kill a lot of people but not strong enough to actually end the conflict. Perhaps unsurprising in a large country of trackless jungle.