New South Wales premier Mike Baird has said he is “incredibly sorry” at the hurt suffered by one mother over the Gayby Baby furore.

Budget estimates hearings are often a dry affair but the questioning took a personal turn on Thursday.

Upper house Labor MP Penny Sharpe – who has children with her female partner – questioned the premier’s handling of a Sydney school’s plans to show all students a documentary that follows four tweens with same-sex parents.

News of the proposed screening at Burwood girls high school hit the headlines and prompted the education minister Adrian Piccoli to direct principals across NSW not to show the film in class time.

Sharpe said she had received a letter from one mother who believed the government had sent a message to children like hers that their families were not normal.

“I want to cry because although I know our child is ever so loved and balanced and sensible, and fully supported as an emerging young person in their own right, I can’t really know what this does to them,” the letter said.

“I am outraged at the media, but more at the damage made so much greater with a government affirmation and intervention that ensured that the message of ‘unacceptable’, ‘not normal’, and ‘tacitly deviant, therefore worth less’ was slammed full force, without consideration, consultation or care, into the minds of children and families throughout the state.”

Baird insisted his government “banned nothing” and that schools were still free to screen Gayby Baby at lunchtime, after school or during classes where there was a clear link between the film’s content and the curriculum.

“I say to her that I’m incredibly sorry,” he said of the letter-writer. “Personally I have to say I was very distressed by the way this played out ... Everyone – every single person – has value. Everyone is normal.”

He added: “The last thing I want is for any family to not feel loved and accepted across NSW.”

Baird drew criticism last week when he was asked about the film and told reporters: “I think tolerance is a good thing. But I think there should be some parameters around it.”