I'm going out on a limb here and hazard to guess that you use clumping litter.
In case anyone else thinks this is a good idea, I can tell you that, as a professional in the field, one should never, ever flush any type of cat litter down the drain. The grit scours the pipes. It settles in low areas and reduces the capacity of the pipe. The treatment plant cannot digest inorganic solids.
Also, do not put cat feces/litter in your compost pile if you use the compost in your vegetable garden. Take my word for it
Oh good, someone I can ask about this... what about animal fat? M had this idea that because emptying the roaster of the cooking liquids is a $&#^# to do any sane way given our home, that flushing it would work. I talked her down... but would it do any serious harm? I have to admit, it would make it easier, but I have my doubts.
I'll give you some general guidance based on the two most common scenarios. Then other people reading might find it helpful. If you need more explanation, please PM me. This is one of my pet peeves because the solution is public awareness and the benefit is to everyone.
Scenario 1 - Your house is connected to a sewer collection system which conveys the sewage to a central treatment plant. FOG is the industry abbreviation for Fats, Oils, & Grease. FOG sticks to the pipe walls, reducing the capacity of the pipe to carry sewage and giving other debris something to stick to. Eventually the FOG builds up into "grease-crete" which is a hard as concrete and can block the pipe, causing raw sewage to flow into basements, streets, and streams/lakes/oceans. This is bad for the environment and exposes the public to disease.
Scenario 1 - Your house has a septic tank and leach field or some other type of individual wastewater treatment system. At least in this situation you only wreck your own stuff by pouring FOG down the drain. It will form a solid layer on top of the septic tank sedimentation tank. It will clog up the leach field. You will pay $$$$ to have it drained & cleaned.
Never ever pour any kind of FOG down your drain. Using cold water and the garbage disposal does not "chop it up finely" and using hot water helps the grease travel farther down the pipe before it cools down and solidifies.
What should you do with animal fats, bacon grease, and used fryer oil? I reuse bacon fat: Cool it slightly, pour into a glass jam jar, and put in the frig for later use in lieu of butter when cooking meat or gravy/sauce. Otherwise use old newspapers. Put a section (at least 5 pages) down flat. Tear another section into strips about an inch wide. Pour the fat over the paper so it is absorbed, then toss in the garbage. In my community, garbage is sent to a waste-to-energy facility so my used oil & old newspapers generate electricity.