The LTM "Manager" authentication role can create iRules.

The Manager role sits above Operator in the BIG-IP privilege hierarchy and is granted full read-write access to all LTM objects, explicitly including iRules. Unlike the Operator role, which is limited to enabling or disabling existing objects, the Manager role can define new configurations such as iRules, pools, and virtual servers. This makes the Manager role appropriate for administrators responsible for traffic management policy.

This is incorrect because the Manager role does possess iRule creation privileges - it is lower-privileged roles such as Operator that are restricted from creating or modifying iRules.