In fact, using an all-white computer monitor is going to enhance this effect, because of the stroboscopic nature of its illumination. It will tend to freeze the moving slit in one spot in your vision, rather than allowing you to correctly perceive the relative movement of the blades.

Here's an easy way to convince yourself: do what you're doing, but start at B and work your way up in speed. Watch how one curtain opens and then the next one closes behind it. You'll get a feel for the cadence and see, as the speeds become faster, how the trailing curtain is getting closer and closer to moving before the leading curtain has gotten fully open, until finally, at just above the flash sync speed, it succeeds in starting before the other one has finished.