dock icons will not disappear when I drag them to desktop or trash

On my MacBook Pro, when I drag an icon from the dock to the desktop or to trash, it bounces back to where it was on the dock. I tried to move Applescript Editor, AppleWorks 6, Keychain Access, Activity Monitor, Quick Time Player and several more icons and they all did the same. Each icon that will not disappear, has a blue dot reflection underneath it.

I moved one of the icons without a blue reflection to the desk top and it did go up in smoke, but as soon as i replaced that icon from finder back to the dock, it also had a blue reflection under it and I could not make it disappear again.

If anyone can help me, I would appreciate it. Thank you so much,

Arudi