This blog post explains how to configure your web browser (Mozilla Firefox or Google Chrome) to prevent YouTube from redirecting from the http:// protocol to https://. The instructions below work no matter if you are logged in to YouTube.
YouTube has started doing this recently in the last couple of months, and also some browser extensions do it now. Please note that using HTTPS gives you more privacy (e.g. governments and internet service providers spying on you) than HTTP, so please think about it carefully if you want to revert to HTTP on YouTube or not.
Test the protocol: Type youtube.com to your address bar, make sure https:// doesn't show up why typing, and press Enter. Wait for the page to load. If you can't see https:// added to the beginning of the address, and you don't see a lock icon on the left side of the address, then we're done, stop.
If you have the Disconnect browser extension installed, disable it. (You may want to enable or reconfigure it later, after finishing these steps.) If Firefox asks for a browser restart, then restart it. Test the protocol.
If you have the YouTube Center browser extension or the corresponding Greasemonkey script installed, configure it by unticking the Use secure protocol checkbox. Test the protocol.
Remove (delete) all your YouTube cookies. In Chrome, copy-paste chrome://chrome/settings/content to the address bar, press Enter, click on the All cookies and site data... button, search for youtube, make sure that nothing unrelated shows up, and click on the Remove all button. In Firefox, open Edit / Preferences / Privacy / remove individual cookies, search for youtube.com, and click on the Remove all cookies button. Test the protocol.
If you're using Firefox on Linux, remove YouTube from the secure site table. To do it, exit from Firefox, and run the following command in a terminal window (without the leading $):
$ sqlite3.static ~/.mozilla/firefox/*.default/permissions.sqlite "DELETE FROM moz_hosts WHERE type LIKE 'sts%' AND host LIKE '%youtube.com'"
If you get an error message and you don't know how to fix it, or you are using Firefox on non-Linux, you can run the same DELETE FROM ... SQL query (between but without the double quotes above) using the SQLite Manager Firefox extension. Test the protocol.
Test the protocol. If it is still redirecting to https://, then take notes which of your browser extensions are enabled, disable all your browser extensions, and restart the browser. Test the protocol. If it's not redirecting anymore, then enable your browser extensions one-by-one, and figure out which one is the culprit. (There may be multiple ones.) Keep the culprit disabled or change its settings.
If it is still redirecting with all your extensions disabled, then this howto can't help you, try to find a solution on the web, and/or ask a question on webapps.stackexchange.com. Don't forget to reenable your browser extensions.
Some anecdotes: on Firefox, deleting the cookies solve the problem for me, and on Chrome disabling Disconnect solved the problem for me.