Better explanation
You can't explain it that way. if the body of the cat remains straight, it can't rotate one part to be upright without another part counterotating, so the cat would either twist right up, or have its back legs up and its front legs down!
Here's a better way to understand it.
The cat flexes its body into an L shape by bending at the mid-body/base of ribs. It then flexes that L, rotating both front and back parts of its body like a pair of meshed gears at 90 degrees. Once both sets of legs face downwards, it straightens up.
There's still something funny going on, but it sorta works...