Cats are intended to teach us that not everything in nature has a function

Humans tend to think that there is a reason for existence. Therefor cats are still trying to give a propper education to humans. So don't think you are adopting and 'educating' a cat, it's the way around: the cat adopts you.

Well, the educational part is a misser. Humans are just not good at learning from their faults. Don't blame cats, they are not all mighty. The next time you see a cat: thank him/her for all the trouble they are through in trying to educate you.