What's your mouse? Logitech? Razer?
https://forums.logitech.com/t5/Mice-and-Pointing-Devices/Right-Click-not-Working/td-p/1136095
http://forums.na.leagueoflegends.com/board/showthread.php?t=3661877
http://www.tomshardware.co.uk/forum/id-2786680/mouse-click-works-intermittently.html
https://forums.logitech.com/t5/Mice-Software/Right-click-problem-in-game-Mx518/td-p/254130
http://www.instructables.com/id/how-to-repair-a-worn-out-clicker-on-an-optical-mou/
Still, a single left click is faster than right click + select.