Why might the united states send military aid to countries that are controlled by military dictators?

The US might send military aid to countries that are controlled by military dictators for humanitarian reasons, or in the belief that regime change would benefit not only the people of that country but also US national security.

The US has given a limited amount of military aid to rebel forces in the civil war in Syria, for instance, because of humanitarian concerns about the brutality of dictator Bashar al-Assad.  One example of that occurred in 2017,  when the Trump administration ordered missile strikes on a Syrian military airbase after the Assad regime had used chemical weapons against Syrian citizens.  (The chemical weapons attack had been launched from that airbase.)

An example of US taking military action for the sake of regime change was the Bush administration's pursuance of war in Iraq.  The belief was that getting rid of Saddam Hussein as dictator would be good for the people of Iraq as well as for the sake of security of other nations, especially the United States.  This sort of policy agenda was part of the "neoconservative" view of a number of  President George W. Bush's advisers -- especially some who had also served in the administration of his father, President George H.W. Bush.  In the wake of the 9/11 attacks, there was a desire to push American values and not be shy about doing so with the use of American military might.  Sometimes referred to as the "Bush Doctrine," the core ideas were that the United States could pursue this goals on its own (without need for United Nations partnerships), that preemptive strikes were allowable against countries that harbored terrorists, and that regime change for the sake of promoting democracy was a good strategy. 

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