Multiple reasons:
1. I have noticed a bug that causes the video to freeze. A work around for the glitch is to maximize the window.
2. You may have autoplay disabled under Safari preferences websites ta or you may have a content blocked enabled. If this doesn't work, download the Safari technology preview or Chrome Canary for free. 6. Try using chrome and see if the problem is replicated.
4. You may have poor quality internet that is causing it to fail to buffer. Make sure flash is DISABLED.
5. Make sure the video does not have a notice saying "full screen mode is disabled." If you maximize a full screen mode disabled youtube video, it will not play at all.