First, before we go any further, we need to understand pressure. Imagine piling sand on top of you on the beach--just a little layer, you don't feel much weight, but as you get buried deeper and deeper, you feel more and more force pushing down on you. This makes sense, since your body has to hold up the weight of all of the sand on top of you.

It's exactly the same in Jupiter's atmosphere--the lowest layer of gas has to hold up all of the weight of the gas on top of it, which means that the core has an incredibly large pressure. Pressurized gasses tend to turn liquid or solid--think of the cans of air that you buy for dusting--if you slosh them around, there is liquid inside, because the air is pressurized to a fluid.

But you are also right to point out that compressing fluids tends to heat them up, and that hotter things tend to evaporate/melt. So, the question is about which trend wins in this case. And for that, the most useful tool we have is a phase diagram. Below, we have one for carbon dioxide${}^{1}$ (source: wikipedia):

Notice that, at very high pressures, the solid state is dominant, even when the temperature is high. The core of Jupiter will be a very high pressure, indeed.

${}^{1}$ Be wary of phase diagrams for water. In many ways, water is an atypical molecule. Non-polar $H_{2}$ is much more similar to $CO_{2}$ than it is to water.

First, before we go any further, we need to understand pressure. Imagine piling sand on top of you on the beach--just a little layer, you don't feel much weight, but as you get buried deeper and deeper, you feel more and more force pushing down on you. This makes sense, since your body has to hold up the weight of all of the sand on top of you.

It's exactly the same in Jupiter's atmosphere--the lowest layer of gas has to hold up all of the weight of the gas on top of it, which means that the core has an incredibly large pressure. Pressurized gasses tend to turn liquid or solid--think of the cans of air that you buy for dusting--if you slosh them around, there is liquid inside, because the air is pressurized to a fluid.

But you are also right to point out that compressing fluids tends to heat them up, and that hotter things tend to evaporate/melt. So, the question is about which trend wins in this case. And for that, the most useful tool we have is a phase diagram. Below, we have one for carbon dioxide${}^{1}$ (source: wikipedia):

Notice that, at very high pressures, the solid state is dominant, even when the temperature is high. The core of Jupiter will be a very high pressure, indeed.

${}^{1}$ Be wary of phase diagrams for water. In many ways, water is an atypical molecule. Non-polar $H_{2}$ is much more similar to $CO_{2}$ than it is to water.