Hi Mohammad,
The Parent role is assigned in the user context (via the child's profile page).
To enable parents to browse the list of users and add users to a cohort, you need to create a new custom role and assign it in the system context (via Site admin / Users / Permissions / Assign system roles. For more details, please see the documentation Creating custom roles.
Moderator note: I am just moving this discussion to the Roles and permissions forum in case you have any further questions.