Interaction pairs- how they can cause movement

Back to basics with this question but I really want to make sure I understand this concept.

Newton's third law states that 'every action has an opposite and equal reaction', which we can see through interaction pairs. However, I'm a little confused on what is happening. I read the answer to 'With Newton's third law, why are things capable of moving?' by Andrew C, however in his diagram, he had a force called F matchbox, and I was just wondering shouldn't the matchbox counteract this force through the interaction pair that it forms?

I find it helpful to visualise concepts, and so basically I have come up with this little thought experiment but I wasn't exactly sure if it's the right way to look at things. Essentially, I imagine a man jumping, and visualise the force the man is exerting on the Earth. I then imagine how silly it would be that the Earth itself moved because of this force, however I then see that the man has risen in the air due to the reaction force. In this way I was able to explain why interaction pairs, even though they are balanced could lead to movement and acceleration.

BTW I realise that a similar question may have been asked before, but the answers I have seen just don't fully explain what's going on and I don't have enough reputation to comment. :(