There is a couple things you can do here...
First you can allow for an empty collection..  
private void DateChanged(CalendarView sender, CalendarViewSelectedDatesChangedEventArgs args)
{
    var myDate = args.AddedDates.FirstOrDefault();
    if (myDate != null)
    {
        string parsedDate = myDate.ToString();
    }
}
Secondly you could check the collection beforehand...
private void DateChanged(CalendarView sender, CalendarViewSelectedDatesChangedEventArgs args)
{
    if(args.AddedDates != null || args.AddedDates.Any())
    {
        var myDate = args.AddedDates.First();
        string parsedDate = myDate.ToString();
    }
}
Some simple debugging would have told you that the issue is probably in the AddedDates property.