<Window x:Name="window" x:Class="SQL_ru__WPF_.ListView_удаление_Item"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:SQL_ru__WPF_"
        mc:Ignorable="d"
        Title="ListView_удаление_Item" Height="450" Width="800">
    <Grid>
        <Grid.RowDefinitions>
            <RowDefinition/>
            <RowDefinition/>
        </Grid.RowDefinitions>

        <ListView x:Name="MyListView" ItemsSource="{Binding MyCollection, ElementName=window}" HorizontalAlignment="Center"/>
        <Button Content="Кнопка" Grid.Row="1" VerticalAlignment="Center" HorizontalAlignment="Center" Click="Button_Click"/>

    </Grid>
</Window>

    public partial class ListView_удаление_Item : Window
    {
        public ListView_удаление_Item()
        {
            InitializeComponent();
        }

        public ObservableCollection<String> MyCollection { get; set; } = new ObservableCollection<string>()
        {   "Январь", "Февраль", "Март",
            "Апрель", "Май", "Июнь",
            "Июль", "Август", "Сентябрь",
            "Октябрь", "Ноябрь", "Декабрь"};

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            if (MyListView.SelectedIndex >= 0)
                MyCollection.RemoveAt(MyListView.SelectedIndex);
        }

    }