Why water can't mix with oil or cooking oil (both saturated and unsaturated)?
The basic answer is that water molecules attract each other and so clump together forcing almost all of the oil out of the clump.
The attraction exists because water is a polar molecule. That is, it has a positive end and an negative end. Thus the molecules tend to clump together just as a bag of small magnets tend to clump together. Oils, on the other hand, are not polar.
This principle can be expanded. In general polar materials tend not to dissolve in oils or, if they are liquids, dissolve in them. The rule in chemistry is "like dissolves like".
The textbook answer for why water can't mix with oil is to use the rule 'like dissolves like'. But a rule in science is none other than summarizing a few collected facts. Answering a question with a rule is like pointing a single fact - why water can't mix with oil - to a collection of facts instead. This easily invites a follow-up question, why like dissolves like. Besides, this rule is vague and superficial; it does not address the facts that
So, IMO, it's better explained in terms of energy. When water clumps with water and oil does the same, the total energy is lower than when they are mixed. The system is more stable if unmixed. But watch for a delicate point in this argument. Energy can be lowered when water molecule is moved into oil molecules. How do we account for it? The lowered energy is not enough to compensate the energy needed to pull that water molecule out of its pool.
However, the difference in energy is not the only factor of insolubility. Temperature plays a role too. When temperature is raised, the difference between dissolved and undissolved states becomes less steep, relatively speaking. When thermal energy chips in, the two substances are more miscible.