I think you are mistaken.

If meat industry disappeared, I don't believe the leather industry would exist on any sort of comparable scale. People would not be raising cows and devoting fields to feed and the whole chain of events that goes into slaughting and animal for it's skin. Leather would be profoundly expensive.

The meat industry on the other hand would be largely unaffected if the leather industry disappeared. They just need to find something else to do with the skin, and they would over night.