Reduces their power--elites in Latin America control economic and political aspects of society. Reforms would provide more groups with rights, reducing the influence of the elite.
In any country, elites often control the means of production and the political system. Reforms, especially coming from lower classes or oppressed groups, would potentially reduce the power and influence the elite group has. This has been true through many revolutionary movements.
The Revolutionary Armed Forces of Colombia (FARC) and the Shining Path in Peru are both communist guerrilla groups. The FARC is a "guerrilla movement involved in the continuing Colombian armed conflict since 1964" and Shining Path is a "Maoist guerrilla insurgent organization in Peru."