In Yosemite or El Capitan, you will not be able to open Minecraft Edu (1.6.4) from the launcher. Follow these steps to fix that issue
Update Tue Oct 6, 2015: the issue was fixed with Minecraft Edu 1.710_20 (here)
chmod +x fix_minecraft_launcher.sh
After the script run successfully, you should be able to open Minecraft Edu from the launcher.