To be unable or unwilling to mix together easily or readily, as of two objects, elements, factors, forces, people, etc. Refers to the natural tendency of oil and water to separate. My dad is like oil and water with my mom's boyfriend, so I don't know how they're going to get through the family reunion in each other's company. The more I pay attention to the news, the more it seems that politics and common sense are as compatible as oil and water.

To be incompatible or unable to interact or coexist easily, as due to fundamental differences in personality, opinions, beliefs, etc. I really wish my boyfriend could get along with my friend Tara, but the two of them are like oil and water.