Your guide is probably in a layer or sub-layer that you have locked.
Layers palette (
Window > Layers or f7) and twirl open (click the triangle) all parts you have locked. There's bound to be some
<Guide>s there, one of them your little cyan offender. Unlock it, select it with the
move tool (or you could just 'meatball' it in the
Layers palette) and hit Backspace.
It's the layer options. If you right click on the layer the guide is on, and click layer options, there should be a checkbox that says lock guides. Uncheck and you are good to go.
You should just drag over the guides that you want to delete or release and press the Delete Key on the Keyboard. Make sure the guides are not locked.