I was always told that if the dog was wagging its tail, it was happy and friendly. If the cat is switching its tail, it was agitated and likely to scratch. I tested this explanation by forcing our happy dog's wagging still. It very quickly became unhappy and bit me. Voila! The adults were right. So, naturally, the next step would be to force the cat's switching tail to hold still and it would be happy... the results weren't what I was expecting.
A childhood belief about cats and dogs

others believed things like this
- We told our little sister that she had a long bushy tail and she fully believed us for ages!!Anon
- When I was very little, I used to believe that bacon came from the tail of a pig because it was curly!!— Audrey
- I used to believe that a cat's butt hole was on the tip of his tail.— PANTS
- I used to believe that if I wagged my dog's tail, it would cheer my dog up.— GED
- I used to believe that if you hit your tailbone, a tail could grow out of it.— Ida
- My Dad convinced me that Manx cats had no tail - and only three legs.— Jim