What’s the meaning of my cat’s ability to do backflips?

My cat’s ability to do backflips is a tactful and funny way to invite others to come to my home.

The full sentence is: My cat can do backflips, would you like to come and take a look?

It comes from a joke: You are on a date with a girl. After the date, you want to take the girl home. You directly say: "Come and sit at my house." The purpose is too strong. You can rephrase it: "Our cat can do backflips, would you like to see it?" Because most people don’t believe it and have never seen a cat doing a backflip, it’s easy to be attracted to take a look.

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So this sentence expresses a feeling of wanting to take someone home and have something happen by the way.

Similarly, you can also say: Our dog urinates upside down. Do you want to go take a look?