You can't do this because you are actually using a data binding, rather than directly assigning values from the start. You have two choices here, either add the items to the collection you have bound to (which should implement INotifyCollectionChanged - ObservableCollection is a good choice here), or you need to use a variation of the following:
ICollectionView view = (ICollectionView)CollectionViewSource.GetDefaultView(listView1.ItemsSource);
var item = view.CurrentItem;
item.Add(....);
There you go, that should help.