Any question answered...

When you've installed a pin it often creates a slightly tight link. If you turn the tool over to the other side, and use the upper part of the cradle you can push the pin back ever-so-slightly in the opposite direction to the way you installed it and it frees it up:

http://www.parktool.com/uploads/images/blog/repair_help/FAQtch3.jpg

this.

but you missed the point about the pressure being applied on the opposite pin.

something like this, if it makes any sense:

http://i.imgur.com/293LOdt.jpg