Yes, as an HR expert, you have the right to reject the manager's request for on-call duty on each Saturday and Sunday. While it is important to maintain open communication and collaboration with your team, it is also important to set boundaries and ensure fair treatment of employees. The expectation of being on call during weekends, without proper compensation, can lead to employee burnout and dissatisfaction. It is crucial to negotiate and establish appropriate terms of compensation and workload redistribution to ensure fairness and work-life balance for all employees.