How did the division of korea after world war ii lead to the Korean War?

The North was led by a communist regime under Kim ll Sung who was supported by the Soviets. The South was led by a nationalist Rhee who was supported by the U.S. Since both wanted to conquer the entire Korean Peninsula and both were aligned with different political ideologies,  it wasn't too unreasonable that Kim decided to attack the South. As a result, America, who adopted a policy of containment under Truman, wanted to expel communist influence as much as possible, which led to America playing a role  in mobilizing a UN force to support the South.  

both believe in many god or polytheism

both built temples that they worshiped in both civilization's god were humanoid

both groups made religion a large portion of their lives

both believe in one religion throughout

the dead were buried with items for the afterlife