Why will ethanol and 1-butanol dissolve in cyclohexane but not 2-propanol?

yes! it has to do with its being a secondary alcohol.

when we say 2-propanol, produced by combining water and propylene. There are two processes for achieving this: indirect hydration (sulfuric acid process) and direct hydration. The former process, which can use low quality propylene, predominates in the USA while the latter process, which requires high-purity propylene, is more commonly used in Europe. These processes give predominantely isopropyl alcohol rather than propan-1-ol because the addition of water (or sulfuric acid) to propylene follows Markovnikov's rule.

Being a secondary alcohol, isopropanol can be oxidised to the ketone acetone. This can be achieved using oxidising agents such as chromic acid, or by dehydrogenation of isopropanol over a heated copper catalyst This is why we couldn't dissolve 2 propanol with cyclo hexane

Howver, we could use cyclohexane to produce pure 2 propanol from wet isopropyl alcohol in the process of azeotropic distillation. cyclohexane here is used as an azeotroping agent.