Why does FSAA make the game so laggy?

Cause the way this setting works is very demanding. It applies Antialiasing in entire image (FSAA - Full Scene Anti Aliasing).
So your VGA needs to calculate how to redraw every single pixel. Each frame.
See.. if your game runs at 1080p@60fps this makes roughly 124416000 pixels draws each second. If you turn FSAA on. Your VGA will need to draw and recalculate each of this 124M pixels per second.