Hey Diddle Diddle

Hey diddle diddle,
The cat and the fiddle,
The cow jumped over the moon.
The little dog laughed to see such fun,
and the dish ran away with the spoon.

"Cat dancing" and "dancing with cats" is not a new phenomenon
The earliest written record of a cat dancing with a person dates from 1692 and evidence of the practice is clearly alluded to in the earliest versions of that rather strange nursery rhyme:

Hey diddle diddle,
The cat and the fiddle,
The cow jumped over the moon;
The little dog laughed to see such craft
And the dish ran away with the spoon

In the original version, which is believed to have been a witches' chant, the opening line is, "Heigh diddle daddle". This is obviously an invitation to the dance; "heigh" being a call of encouragement and to "diddle daddle" meaning to shake or move from side to side in a series of jerks.
("Diddle daddle" was later changed to "diddle diddle" around 1760 when it was popularized as a nursery rhyme so as the first line would rhyme with "fiddle" in the second.)
The earliest version of the second line reads, "The cat's fiddle faddle" which is a derogatory reference to the nonsensical craze of joyful leaping about with cats. A later version of the second line reads, "The cat has the fiddle", which refers not only to the wailing fiddle-like sound the cat makes but also to the fact that it is possessed of a kind of musical power which is able to get us up and dancing. The use of the word "catgut" to describe what the strings of a violin are made of, when they are actually made of sheep's intestines, is further evidence of a belief in the musical or bewitching qualities of the cat¹s inner being.

"The cows jumped over the moon" tells of the way in which cats are known to "spook" cows in the fields at night and send them rushing madly about. However, there is a clear inference here that the cows are willing partners in this "dance" and even today being "over the moon" means being deliriously happy.

"The little dog laughed to see such craft" is a clear reference to Canis Minor or Procyon, the Lesser Dog Star in the constellation of the Little Dog. The suggestion here is that this "craft" or art has a far wider cosmic link and implies that the power of the universe is able to be channelled positively by dancing with cats.

"The dish ran about like a spoon". "The dish" here, is another name for a maid, usually a milk maid, and a "spoon" or spoony is an archaic term for a crazy person. So in this last line we have cat dancing making the maid rush about like a crazy person.
The verse clearly suggests that the practice of cat dancing can have negative consequences especially for females, leading not only to lunacy in cows, but in the case of maids, to a complete loss of proper muscle control. There is little doubt that this was precisely the message the verse was designed to convey and it is likely to have been vigorously promoted by the Church in the middle ages as it wished to encourage the belief that, "...those who durst jig by the cat do cavort with the devil hemself"."