Heather Dinich explains that DJ Durkin's job status with Maryland is still one of the biggest questions in the Jordan McNair case. (1:23)

The parents of Maryland offensive lineman Jordan McNair, who died in June from heatstroke caused during a team workout, say the toxic culture in the football program played a role in their son's death and that DJ Durkin should no longer be allowed to coach.

"He shouldn't be able to work with anybody else's kid," Martin McNair told ABC's "Good Morning America" on Thursday. "You send your kid away to college for them to be developed into young people -- and that's physically, emotionally and spiritually. And teach our young kids, our young people that we worked so hard to get there.

"'Hey, I'm giving my child to you. Keep him safe.' They did anything but that. So of course he should be fired."

Jordan McNair and other linemen were completing a sprint set on May 29 when McNair started showing signs of extreme exhaustion and had difficulty standing upright. Billy Murphy, an attorney representing the family, has said that McNair had a seizure, but a 911 call, obtained by ESPN, wasn't made for another hour.

Murphy has also called for Maryland to fire Durkin.

Details about McNair's death were reported at the same time as an ESPN investigation into the culture at Maryland that included the use of fear and intimidation toward players via extreme verbal abuse and other methods.

Multiple sources told ESPN that head athletic trainer Wes Robinson yelled "Drag his ass across the field" about a struggling McNair and that trainers were working to keep the lineman upright.

McNair's mother, Tonya Wilson, told "Good Morning America" that her son wouldn't have stopped, in part due to the ridicule he might have received.

"Jordan was the type of person, he would give his all, he would give his best because someone asked him to do something," Wilson said. "He would always give his all. He wouldn't have stopped. He wouldn't have stopped. If that's the culture, then he didn't want to be called any names, things that they say they've been called."

Durkin has been placed on administrative leave as the university investigates McNair's death and the allegations of abuse and disparagement. On Tuesday, university president Wallace D. Loh said the school accepts responsibility for McNair's death.

The school has parted ways with Rick Court, the assistant athletic director for sports performance. Two members of the Maryland training staff -- Robinson and director of athletic training Steve Nordwall -- are also on administrative leave.

Information from ESPN's Heather Dinich was used in this report.