The 94-year-old Nobel laureate spent his sixth day in a hospital Thursday, being treated for a recurring lung condition.
President Jacob Zuma said Wednesday Mandela is "responding better" to treatment and officials are "very happy" with his progress.
Some South Africans said a person's illness and death should remain private and they're skeptical about reports he is doing better, USA Today reported.
"This is a man who gave so much of himself to this country," said Roseline Wilson. "He must rest. He has suffered too much in his old age."
In South African culture, the dying or very sick can't die unless their family releases them or gives them permission, USA Today said. Once the family gives permission, it's as if they are telling the person they can survive without him or her.
South African culture also says it's not respectful to talk about a person's death until afterward.
"I don't think he is getting the right respect that he deserves," said Darko Destanovic, 28. "Everyone is sitting on the edge waiting for him to die as if he was a spectacle. People want him to stay alive for themselves, not for him."
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