As we well know, oil and water don't mix with each other, and the density of cooking oil is lower than that of water. Thus, the oil poured can create a film on top of sewage water, hindering its oxygenation. In an atmosphere lacking oxygen, there are microorganisms able to transform the organic matter dissolved into methane, which has a Global Warming potential 23 times higher than CO2!
Once arrived to the sewage water treatment plant, the oil is already dispersed into drops which reduces the efficiency of the first treatment processes. In the end, it may oblige to add specific oil removal stages, excessive for a simple domestic sewage water plant. Later in the process, it can hamper digestion of organic matter during the biological treatment, as it disturbs regular bacterial development. As a result, it increases costs and may give rise to higher taxes for compensation (so called "externalities").
Finally, it can get stuck to your pipes, creating a crust, and trapping or retaining particles, dirt, and waste, resulting in bad smells and poor hygienic conditions for your home.
So, what to do with this oil if we don't want to use it?
Eco-tip: Oil is a problem for a water treatment system. However, it is also a great biofuel. Thus, why not taking advantage of it through energy recovery?
Cooking tip (extra):
Put the oil in a salad or use it for a marinate (especially if it's olive oil). It will give to your dishes a delicious fishy taste.