Try it in different way and Use below code in xaml file:
<toolkit:ListPicker Width="220" Name="monthCat" VerticalAlignment="Center" Height="58" ExpansionMode="FullScreenOnly">
<toolkit:ListPicker.ItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding}"/>
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.ItemTemplate>
<toolkit:ListPicker.FullModeHeader >
<DataTemplate>
<TextBlock Text="{Binding}" FontSize="28"/>
</DataTemplate>
</toolkit:ListPicker.FullModeHeader>
</toolkit:ListPicker>
Use below code in .cs file
string[] monthName = {"Select", "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"};
int month= DateTime.Now.Month;
monthCat.ItemsSource=monthName;
monthCat.SelectedIndex = month;
monthCat.UpdateLayout();