Why are some solutes soluble in water and others in cyclohexane

The answer to the question is due to the ability of the solute to form interaction with the solvent. Some solutes (hydrophylic) are able to form bonds with water molecules and so dissolve, while others which are not able to dissolve in water (hydrophobic) are able to form bonds in non polar solvents such as cyclohexane

Explanation:

A solution is formed by the interaction of the solute particles with the solvent such that the particles of the solute freely diffuse through out the solvent.

However, some solute are hydrophilic (easily attracted to water) while others are hydrophobic (repels water). The hydrophilic solute is a polar solute that has an NH or OH bond  and easily forms hydrogen bonds with water molecules. The hydrophobic solute, which may be polar, consist of mainly CH bonds which do not dissolve well in water but dissolve in solvents such as benzene and cyclohexane with which they form interactions including Van Der Waals forces.