This is a wonderful congruent conflation (a malaphor involving two phrases with the same meaning) of “oil and water don’t mix” and “like fire and ice”, both meaning opposites or not getting along. The expression “they are like two peas in a pod” has the opposite meaning but could have first jumped into the speaker’s brain as she started out by saying “they go together”. However, the context was a discussion about two co-workers who did not get along and bickered a lot, hence the confluence of similar meaning phrases. A big thanks to Elissa who posted this gem to the website!
What does happen when oil and ice come together? Well, physicscentral.com says the following:
Both oil and ice can be slippery, but this is where the similarity ends. Oil and ice have very little in common. Actually, oil doesn’t like ice, or more specifically melted ice, water. Oil is known as hydrophobic, meaning that it repels water. When you put the ice cube in the oil it begins to melt. It doesn’t mix with the oil because oil is hydrophobic. This explains why the oil and water don’t blend together, but this doesn’t explain why the water goes to the bottom of the cup and why the ice floats at the top of the cup. This is all comes back to density, or how much stuff is in an object. If something is denser than something else, it will sink. Water is denser than oil; that’s why water sinks to the bottom of the glass. Ice, however, is a funny solid. When water freezes and turns to ice, it actually takes up more space than it did when it was water, but it has the same amount of stuff in it. This means it is less dense than water. That’s why ice cubes float in your water glass. Since ice is less dense than water, the water settles to the bottom. Since the ice is less dense than water and therefore less dense than oil, it floats at the top.