Thought the language is a bit confusing, if you check the Codex and pay attention to the difference between the Admin and the Super Admin you should be able to see what is happening.
In the case of single site WordPress installation, Administrators are,
in effect, Super Admins. As such, they are the only ones to have
access to additional admin capabilities.https://codex.wordpress.org/Roles_and_Capabilities#Super_Admin
And…
Only Administrators of single site installations have the following
capabilities. In Multisite, only the Super Admin has these abilities:
- update_core
- update_plugins
- update_themes
- install_plugins
- install_themes
- delete_themes
- edit_plugins
- edit_themes
- edit_users
- create_users
- delete_users
- unfiltered_html
https://codex.wordpress.org/Roles_and_Capabilities#Additional_Admin_Capabilities
That last capability is the issue.
unfiltered_html
- Since 2.0
- Allows user to post HTML markup or even JavaScript code in pages, posts, comments and widgets.
- Note: Enabling this option for untrusted users may result in their posting malicious or poorly formatted code.
- Note: In WordPress Multisite, only Super Admins have the unfiltered_html capability.
https://codex.wordpress.org/Roles_and_Capabilities#unfiltered_html
Only Super Admins have the capability you want, and you are an admin. Unless you have access to the site’s code to add that capability to the ordinary blog Admins, or just to your particular user, you won’t have unfiltered_html capability.