I know they can't grow in places that aren't hot, by why exactly can't they?
Palm trees are not necessarily tropical. I live in Arizona and it certainly is not tropical here.

They are not frost-resistant.
Their cells use enzymes which function better at warmer temperatures.

bcuz they're tropical?

Palm trees are unlike average trees. They do not grow rings the way true trees do on a yearly basis. Instead they are more similar to grasses and reeds, in a perpetual state of growth. In cold climates trees slow photosynthesis during cooler/ cold months. If a palm tree stopped photosynthesizing, because of the plants lack of rings, the palm tree would loose internal water pressure, wilt, and fall over. That is why Palm trees cannot survive outside in cold climates.

Palm trees do not have a dormancy period, and therefore their cells freeze and die in colder climates. Plants that survive the winter usually convert the liquid in their cells into a form that is similar to antifreeze. This keeps the cells of the plant from being damaged. As the weather warms up the antifreeze material converts back.