On YouTube, there are two licenses to choose from, Creative Commons license and Standard YouTube license. Suppose that a composer A wants to post A's music videos on YouTube, but wants to license my music under a different term. Can A just directly state the license in the description, or A would still lose my copyright no matter what? I know copyright can be lost if one licenses their work under CC. Would A lose rights because A posts work on YouTube.
The YouTube Standard License is described in the terms of service. It means that you retain your copyright:
you retain all of your ownership rights in your Content.
But you also grant YouTube very broad permissions to your content:
by submitting Content to YouTube, you hereby grant YouTube a worldwide, non-exclusive, royalty-free, sublicenseable and transferable license to use, reproduce, distribute, prepare derivative works of, display, and perform the Content in connection with the Service and YouTube's (and its successors' and affiliates') business
Yes, that means YouTube could allow others to use your content by "sublicensing" or "transferring" their license. I never heard of YouTube doing that, but the license terms would allow it if they would decide that they want to.
But without an explicit permission from you or from YouTube, people are not allowed to reproduce your content.
Agreeing to those terms (or alternatively to the Creative Commons CC-BY terms which do allow others to use your content as long as they give attribution) is a condition for using the platform.
You can also put different license terms into the video description. This is called "dual licensing". But that means that people get to choose under which license terms they want to use the content. They can either use YouTube's terms, or your own.