The SelectedItemChanged event is not firing when you click on arrows. Only the SelectedIndexChanged event is firing.

Resolution: 
The SelectedItemChanged event should be fire only if user click on the item and the ItemClickDefaultAction property is set to SelectItem mode

FIX. RadCarousel - SelectedItem is not assigned when the control is started.

Resolution: 

Selected Items represents the Clicked by mouse item and this behavior is a desired behavior.

So it should be not populated without user click on an item:

Instead the users should use the SelectedIndexChanged event in order to detect the current item:

        private void radCarousel1_SelectedItemChanged(object sender, EventArgs e)
        {
            currentItem = radCarousel1.Items[radCarousel1.SelectedIndex];
        }