This question is asking for a subjective answer about events that occur during chapter 16 of Andy Weir's book The Martian. The book was later adapted into a film, and the movie also did an adequate job of showing this difficult decision to audiences.
Guo Ming from the China National Space Administration figures out their space probe, Taiyang Shen, has adequate fuel to be sent to Mars to resupply Watney. The probe would need some modifications, but it is possible. Ming alerts NASA to the possibility, and NASA agrees it is possible; however, Watney would run out of food a few weeks before the probe arrives. The alternative plan, supported by Mitch, is to use the Taiyang Shen to resupply the Hermes because Rich has figured out a way to get the ship back to Mars before the Taiyang Shen would have arrived.
Mitch argues in favor of the Hermes rescue option, but the NASA administrator decides against it. He argues that risking the entire crew of the Hermes is a bad idea, and he is right. Losing Watney is terrible. Losing the entire crew is worse. He is choosing the needs of the many instead of the needs of the few, and I think his decision shows wisdom and strength. Mitch believes it is cowardly, and Mitch sends the plans for the second option to the crew of the Hermes. They change course the next day to have the chance of saving Watney. Mitch always believed it wasn't NASA's decision. He wanted the crew to decide if they were willing to risk their own lives to save their fellow crew member. Mitch's actions went against protocol, but he did the right thing by giving Watney's friends the option to put their lives in danger for a rescue mission.