Happy Friday - what we have here is "dog yoga".
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Since it's Friday, I'll note that the dog here is named "Montana" and is a French Bulldog.
And this one is named "Satchmo".
Begin mocking this at will. I don't think the dogs should be involved here. Clearly the dog will be unhappy about being turned upside down for no particular reason. He could get hurt. And Montana up there is being unwittingly put in a dog-dominant position. Keep that up, lady, and he'll be humping your leg in no time, and then sorry won't be enough.
But for the counter-argument, it's simple: include your dog in everything you do, even if it's silly... and both of you will be happier for it.