Why do molecular compounds have low melting points and low boiling points relative to ionic substances?

Because the intermolecular forces between the molecules of the compound are much weaker than those between ions in the ion substances. So, it takes less energy for them to move apart and thus they separate and become liquids or gases at lower temperatures.

Intermolecular forces among molecular compounds are usually quite weak, consisting mainly of dipole-dipole forces, and of course, the much weaker London Dispersion Forces. Since these forces determine how strongly molecules of the same molecular compound are attracted to each other, and because intermolecular forces among these molecules are so weak, it is easy to boil them. Take CO2 for example; it is a linear, nonpolar, molecular compound with weak intermolecular forces that allow it to boil with ease at very low temperatures. Its boiling point is around 217 Kelvin, clearly showing that its physical structure as a linear, nonpolar molecule will cause it to have a low boiling point. On the other hand, ionic bonds depend on the charge separation between the cation and anion, which are VERY STRONG when compared to the very weak intermolecular forces of any compound, whether it be ionic or molecular. Hence, the higher the charge separation in the ionic compound, the higher the melting/boiling point of the ionic substance, and as a result, have much higher melting/boiling points than molecular compounds.