No one knows exactly why people refuse to be organ donors. Organ donation is a tricky subject, and super individual.
According to one study most people gathered information on organ donation by watching scientifically inaccurate shows like Grey's Anatomy.
Another study backed up that data, showing more than half of people learned what they know about donation from television, and another 12 percent from their friends; unsurprisingly, 72 percent of people were afraid organ donation.
First, if a patient enters a hospital, literally no one is thinking about whether or not they are an organ donor. If it's an emergency, they're working to save the person's life, if not, to try and make them healthy again. And yet, it's a fact of life that they don't always succeed. If the person does die, only then do they check if the person was a donor.
organdonor.gov: Organ Donation Statistics
University of Miami: American Academy of Neurology Guidelines for Brain Death Determination
BMJ: Death, dying and donation: organ transplantation and the diagnosis of death