For my fellow college students struggling to write papers, I have found a way to remove a horizontal black line that is not selectable or be deleted.
Please note that this is based on a Mac version of Microsoft Word 2008.
However, there is a way to remove those lines. This is how:
1) Select the area above and below line you want to remove.
2) Select Format from the very top.
3) From the drop menu, select Document…
4) In the popup window, select border…
5) In the new window, select none from the column in the left.
6) Click okay.
And your annoying border should disappear.
Hope this helps you!