If your role is 'Trainer' in the Training function, you cannot operate the 'Show only the teams I belong to' checkbox in the 'Team Management' screen.

Trainers can only check the progress of the teams they belong to.
If the team you want to check the progress of is not displayed in the 'Team List' within 'Team Management', please take either of the following actions:
Join the target team
By joining the target team, the team will be displayed in the 'Team List'.
Please ask the Group Administrator or Group Sub-Administrator to perform the operation.
Related: Edit Team (Web Browser Version)
https://teachme.jp/8/manuals/42393945
*If you are a Group Administrator or Group Sub-Administrator, you can add your own account to the team.
Change your role to Training Administrator
By changing your role from 'Trainer' to 'Training Administrator', teams you don't belong to will also be displayed in the 'Team List'.
Please ask the Group Administrator or Group Sub-Administrator to perform the operation.
Related: Add or remove training administrator or trainer (Web Browser)
https://teachme.jp/8/manuals/9316199
*If you are a Group Administrator or Group Sub-Administrator, you can change your own role.
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Related: About training function permissions
https://help.teachme.jp/hc/en-us/articles/900006442583