As I said above, a worn chain will wear out a cassette much more than a worn cassette will wear out a chain. A worn chain stretches, so it doesn't sit exactly on the teeth of the cassette, and this wears a bigger U shape between each pair of teeth. Eventually though, the chain stretches so much that it can't sit on even the worn U shape, and starts skipping.
The same doesn't happen in reverse. A new chain may not like the worn U shapes of an old cassette and may skip, but they're not damaging it much - the centres of the teeth are still the correct distance apart for a new chain, so they aren't stretching it.
