Sadly it's not a very good ATX Pin Remover that comes with that kit as the prongs on the tool are too thin to depress the tangs on some pins.
Make sure that you push the wire back up into the housing then press down the tool to make sure the tangs are depressed. Also pull the wire straight when removing it and you may need to 'wiggle' the wire first. You may need more force than you think to remove the pin but there's also a risk of the wire coming out of the pin.
Someone bent the prongs on one of those tools to make it work better. I'll try and find the link.
Edit: Not a great photo
but probably enough to give you the idea of how to bend the prongs on the tool.Edited by Big Elf - 10/2/13 at 7:08am