Ms Couch, who became world welterweight champion last year, is accusing the British Board of Boxing Control of sexual discrimination by stopping her earning her living as a professional fighter in her home country. Her fight is being backed by the Equal Opportunities Commission.
Dr Whiteson told the tribunal in Croydon, south London, that he had no objection to women boxing and saw no reason why they should not establish their own professional authority with its own medical advisers.
"However, boxing as we know is a high-risk sport which can cause injury and death. Should such a tragedy occur when a woman is boxing, I believe the public adversity would put the whole sport at risk."
Earlier the tribunal heard Dr Whiteson say he considered women in general "too frail" to box because they bruised easily and became emotionally unstable and more accident-prone during menstruation. Another argument by the council is that women might unintentionally box during early stages of pregnancy. Attention is also drawn to some medical opinion which contends that repeated blows to the breast can cause lumps which may turn malignant.
Dr Whiteson, who has 35 years' experience in the sport, confirmed that women were not considered individually by the council; they were banned as a gender.
"We have no evidence to show that women's boxing is safe. We have a totally open mind, but there are doubts and I have to defend the sport of boxing to my peers and to the press."
Ms Couch, 29, known as the "Fleetwood Assassin", was told by Dr Whiteson that she might thank him in the long run. "It is possible that if research proves increased risk to women, we may have done the applicant a great favour." The 10-stone 5ft 7 in boxer took up the sport three years ago after seeing a television documentary about female fighters. She won her world crown in Copenhagen last May by defeating reigning champion Sandra Geiger. John Warren, chairman of the tribunal, later reserved judgment.