Appearing before an employment tribunal, Hunt responded to claims of age and sex discrimination from former Countryfile presenter Miriam O'Reilly, 53.
Hunt, 43, has been blamed for the decision to ditch O'Reilly and three other female presenters, all over 40, when the show moved to a primetime slot last year.
O'Reilly previously told the tribunal in central London that Juliet Morris, another of the sacked presenters, had told her that Hunt got rid of them because she "hated women".
However, Hunt said that the allegations were "categorically untrue, profoundly distressing and utterly offensive on every level".
"I am a 43-year-old woman. I have had my own difficulties surviving this industry and for that reason the last thing I would ever do is discriminate on the basis of gender or age," she said.
"The only small comfort I have taken from such a distressing thing as this is the number of women, both behind and in front of the camera, who have got in touch - sympathetic and outraged that I have had to sit there and listen to such a hateful thing."
Asked whether she was alarmed by the prospect of four older women leaving Countryfile at the same time, Hunt said: "It didn't cross my mind."
Addressing O'Reilly's legal representative Heather Williams QC, she said: "If I had clocked this number of women of a certain age would be disappearing as a result of the criteria [set for the new show], I may well have remarked on it.
"You may well argue that it was stupid of me no to clock it. You put it to me that I should have realised that it would have impacted on women. Unfortunately I didn't realise that."
Hunt said that O'Reilly was "completely unknown to a peak-time audience" and did not have the "skill level" to be taken forward for the new show.
"She is an extremely talented television reporter. She is not a fantastic, immersive presenter. That is not her strength," she said.
"If Ms O'Reilly met the criteria we had set for the new Countryfile we would have had absolutely no hesitation in using her. Indeed, I would have actively welcomed having a woman over 45 in the mix of faces."
Hunt, who is on gardening leave before joining Channel 4 in January 2011, also said that being controller of BBC One is like facing "incoming fire from the press on a daily basis".
She added: "In my time on BBC One it was pretty rare for a story to break in the way we would have wanted. That type of incoming fire is part of the meat and drink of everyday life."