I think you may have forgotten what it's like to be a young person encountering new technical concepts for the first time. Or maybe you were fortunate enough never to have encountered a misleading description, or maybe you were smart enough to think beyond every misleading decription on your own every time. Most people are not so fortunate.
The problem here is not that the article uses an analogy, the problem is that it doesn't present it as an analogy, it presents it as literal. The headline says that mathematicians have measured a force. That's nonsense. They did no such thing. But in order to realize that they did no such thing and that the "repulsive force" idea is an analogy you have to already know what is going on.
Here is another example from the body of the article:
"“You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said.
No, you can't. If you could, then the "force" that these "particles" exerted on each other would cause them to move in accordance with Newton's first law. So not only is it an analogy presented as literal, it's actually a bad analogy.