Why are there states of matter?

We all learned in school that there are three states (or phases) of matter: solid, liquid, and gas. Later, you may have learned of a fourth state, plasma; and, physicists say there various other states that emerge in extreme conditions (e.g. Bose-Einstein condensate). But let’s keep it simple, and go with three for now.

While helping my 12-year-old son with his homework, this question came up, and I haven’t been able to find the answer:

Why are there states of matter at all?

In other words, it’s easy to imagine a physical world where there are no phase transitions. In this alternate world, all matter would change continuously with temperature change. The molecules of the substance would continuously increase in space from one another, with no sudden changes in properties or structure. At the coldest temperatures, everything would be extremely solid. As the temperature warmed up, the solid would become progressively and continuously less solid, and more “mushy,” let’s say. More “liquid like” but continuously, not in a sudden phase transition. And as this liquid-ish form of matter warmed up into what we know as the “gas” state of matter, it would gradually and continuously become more fog-like–but again, with no sudden phase transition.

I have searched all over the Internet, and I haven’t found this question asked or answered. (I ended up reading some advanced stuff about energy states, and curves crossing, but that doesn’t answer the question.) Does anyone know the answer, and if you do, can it be explained in a way that regular people can understand it?