By default, your pre-recorded and live stream videos hosted on YouTube will have the option to embed enabled. If you are experiencing issues with your video or live stream displaying within the session, it may because this setting has been disabled and is preventing the content from being shared in this way.
To check on the status of your account features, visit https://www.youtube.com/features?nv=1 and confirm that Embed is listed as enabled.
If your Embed setting is not listed as enabled and you are unable to change the status, it is likely because your YouTube account is ineligible for Monetization. Livestream videos in particular, must be set for monetization in order to support embedding. To qualify, an account must have 4000 or more hours of public watch time within the last 12 months, and 1000 or more followers. Note, that some older YouTube accounts may not be impacted by this policy.