Why prefer composition over inheritance? When is inheritance actually the right tool?

class CountingSet<E> extends HashSet<E> {
    private int adds = 0;
    @Override public boolean add(E e) { adds++; return super.add(e); }
    @Override public boolean addAll(Collection<? extends E> c) {
        adds += c.size(); return super.addAll(c);   // HashSet.addAll calls add()…
    }                                               // -> every element counted TWICE
}

// Composition (forwarding) is immune to the superclass's self-use:
class CountingSet<E> implements Set<E> {
    private final Set<E> inner;                    // delegate
    private int adds = 0;
    public boolean add(E e) { adds++; return inner.add(e); }
    public boolean addAll(Collection<? extends E> c) {
        int before = adds; boolean r = false;
        for (E e : c) r |= add(e);                 // OUR contract, our counting
        return r;
    }
    // …forward the rest
}