When I shared a youtube URL, there is thumbnail image instead of an embedded player. Hence, every time you click on the thumbnail, you're redirected to youtube website. You can't play it directly on Facebook. The URL shared might look like following:
What I want it to be is:
The reason is the video owner disabled embedding. We can't do anything about that if we're not the owner. You can see whether the embedding is enabled or not by clicking on the Share icon then Embed and you'll see as in the image below if embedding is disabled.
If embedding is enabled, you'll see as following:
You might have to look for another video that embedding is enabled.