Hi Starfox,
Let's start with changing the settings of your FCP sequence, they are completely wrong.
Let me explain:
Your Frame Size and your Aspect Ratio are set to 1280x720 and HDTV 720p, which is correct for outputting an HD 720p video to Youtube.
However, your Pixel Aspect Ratio is set to NTSC/DV - anamorphic which is a non-square aspect ratio. For a correct display of 720p on a computer your Pixel Aspect Ratio should be Square and NOT anamorphic.
Furthermore your Field Dominance is set to Lower, which is inconsistent with 720p (Progressive).
And finally your editing base is set to 25 fps (PAL), while your Pixel Aspect Ratio is set to NTSC.
All these inconsistencies can cause your video to export with a wrong pixel ratio, which can cause the borders you see in your Youtube video.
So do the following: Open your sequence in FCP, select Sequence > Settings and enter the settings exactly as you see them in the attached picture.
You may have to re-scale your still in FCP after having changed the settings because all these inconsistencies can cause your image to display improperly. Once your settings are changed and your still fits the entire Canvas, Share to Youtube and see if the video displays correctly now.
Best wishes,
Ronny