This is quite a difficult question to explain without images but here goes...
I understand that when you focus on an object in the foreground any objects in the background are doubled, so if you look at your finger close up you see two chairs in the background where there is only one, and I know that this is beacause both eye's alignments are pointing at the finger so behind the finger they cross etc, but...
When you close your left eye, instead of the chair on the right disappearing (which as far as I am concerned should happen) the chair on the left does?

Pretty trivial, I know, but just always puzzles me.

Right first off if your looking at your fingers and you see chairs something's wrong lol

Okay, as you are looking at your monitor, put your finger up in the middle, and focus on it, now you know your left eye is looking to the right of the monitor, and your right eye is looking to the left of the monitor. Therefore the image of the left eye, must be the one where the monitor is left most! And the right eye is giving the image where the monitor is right most!

This is quite confusing, it's because you have to remember that your brain is molding both eyes into a single image.

This explains well what youa re seeing.