Why did the UN not stop the genocide in Rwanda?
Basically, the UN did not do enough to stop the genocide in Rwanda because the most important countries in the UN (in particular the members of the Security Council at the time) did not really have the will to do so.
The UN, as an organization, cannot really do anything unless the member nations want it to. The UN has no army of its own to send into a place like Rwanda. Instead, it has to rely on individual countries to send troops to enforce UN resolutions.
At the time, the most important countries in the UN (like the US) simply did not want to send troops to Rwanda. They did not care enough about what was going on and they worried about the costs of intervention and how it would be perceived if Western troops interevened in the domestic affairs of an African nation.