You need to push until the first major resistance - some stop there thinking it's in, but it's not, at least not properly. It then needs a much firmer push to open up the very tight jaws to make a proper grip on the pins. As you do so you'll see the back part of the plug push backwards.
Just be sure you are holding on to the front of the kit because otherwise the force needed will send it flying off the shelf. Also make sure you only handle the outer case of the IEC (i.e. don't push from the back), otherwise the back end of the plug won't push back and decouple properly.