Mr VIreland has it mostly covered but also Chedder is correct.
To put this differently -- push *in* with the wire in the opposite direction of the red arrows in post #4. This will prevent edge of the tang from getting hung up on the housing. Then push the tang in with a screwdriver (green arrows shown in post #4). With the tang pushed in - then pull the wire out in the direction of the red arrows.
Sometimes if you push the tang in without pushing the wire in first - the tang will snag on the housing and bend so that it buggers the contact when pulling.
Push in wire, push in tang, pull out wire.