You didn't get Compressor by chance along with FCPX, did 'ya

???
Anyways, if you have 10.1.x, give this a try...
1. Go to "File -> Share -> Add Destination...".
2. In the pop-up window that shows, click on "YouTube".
3. Make sure all of the settings are correct (1920x1080 or 1080x720/Better Quality/Private/etc.).
4. Click on the "Details" button in the upper-left corner.
5. Enter the login and pass you use for your YouTube account... the login is the primary email address you use to login to the YouTube/Google webpage and NOT your user name.
6. Close pop-up window.
7. Go to "File -> Share -> YouTube..."
8. Now try uploading and see if it works

. I had the same problem in the beginning and the solution was not always the clearest

.....
Best of luck ^_^ !