From the YouTube app.
When it tries to send the email, tap and hold on the URL {http...} in the body of the email. When the pop up menu appears choose Select, drag the handles to highlight the entire URL, then choose copy.
Cancel the email, delete the draft, and close the YouTube app.
Now go to FaceBook in Safari, choose to post a link (at top of page). When the URL field shows up tap and hold until you get the popup menu, and paste the URL. Add your comment and you are good to go. Or you can use your favorite FaceBook app, if it supports posting links.
Or, you can just go to YouTube in Safari and share it from there. Works fine, though the desktop version of the site has that ugly Playlist gadget cluttering up things.
You can go to a prettier, but less versatile, YouTube page by using the link m.youtube.com
Both will require you to sign into Facebook if you don't have the accounts linked.