For some reason my cat thinks she is a hunter. This is despite the fact that she once attempted to kill a spider for 15 minutes only to eventually lose it under the fridge. It doesn't matter, because in her mind she is the greatest hunter the world has ever seen and she likes to show it off by attacking the cursor on my computer screen daily. This inspired me to create a cartoon about what cats are thinking when they're viciously attacking their harmless toys.
You can check out more of my animations here.
If you're looking for the actual answer to why cats play with string I was able to find a few answers online that I found interesting. One was in the wild cats compete with snakes for food. So cats will instinctually kill snakes so they don't eat their food and that instinct is so strong that cats have a desire to attack any snake like object such as string. You can read more about cats behavior here.