Why Do we Refer A Cat Having Nine Lives?

I have been hearing that about cats most of my life.I think they have a time that they live and then they approach the latter stage of life,like humans.

That I believe was an old folk tale although they did believe it to be true.

An ancient proverb says a cat has 9 lives. For 3 he plays for 3 he strays and for the last 3 he stays.
I think the main reason is they have flexibility and agility . We had a cat and we lived on the 6th floor. Cats always sleep with their eyes closed and he slept on the lana. One morning we looked outside and he was not there. He fell all the way down to the ground. He only had a few scratches other than that he was fine. This is a true story.