I'm focusing, not on the particulars of the illustration you mentioned, but the general logical fallacy.
This is logically fallacious. I have given a significant amount of thought to this particular fallacy and don't know whether it has been named. I started thinking about it back when I was a JW and encountered people in the ministry who would use illustrations to try to prove the Trinity doctrine. I was once working with my long-time JW grandfather in the door-to-door work. He encountered a man who told him that the trinity is like an egg.... there are three parts - white, yolk, and shell - but they make up one egg.
My grandfather was frustrated, and later he asked me "How can I counter that?" After thinking about it, I realized that illustrations don't prove anything; they simply can help people to understand a point one's making whether that point is true or not. The answer my grandfather could have given to the man is "No, it's not like that."
Here is an example of an illustration that's wrong: Many of us might remember being taught in school that electrons orbit the nuclei of atoms like planets orbit the sun. We might remember images like this:
The problem is, though, that it's simply not true. The illustration is completely wrong. Electrons are not little particles that orbit around in paths as shown in the image. They do not behave that way at all. They are not in any way like planets that behave largely according to classical mechanics. They don't even follow certain paths. They obey quantum mechanics. One can only speak of the probably of finding an electron in a certain place at a given time, and the probability clouds look nothing like the orbitals shown above.
So, the fact that one can produce an illustration to try to prove a point in no way proves that point. The fact that one can say that electrons orbit nuclei as planets orbit the sun proves nothing.
One could simply and easily and logically correctly refute her by saying "No, they're not like drunk drivers."