A woman who contacted the police after a journalist wrongly accused her of mutilating and castrating her trans daughter says she will withdraw her complaint because the case was leading to the spread of misinformation.

Susie Green, who is chief executive of the transgender children’s charity Mermaids and whose daughter Jackie is transgender, said that she had decided to withdraw the complaint against Caroline Farrow because of widespread reports that the dispute had only been about “misgendering”.

“If I had continued my complaint then [Farrow] would have continued to have a platform to spread misinformation about what actually happened,” she told the BBC Two’s Victoria Derbyshire programme. “Being involved in an investigation would have meant that I couldn’t talk.”

Farrow, a Catholic commentator and broadcaster, had been contacted by Surrey police and asked to attend a police interview over a series of tweets about Susie and Jackie Green. On Tuesday Farrow posted that she did not “remember said tweets”, adding: “I probably said ‘he’ or ‘son’ or something. All I have been told is that following an appearance on Good Morning Britain I made some tweets misgendering Susie Green’s child and that I need to attend a taped interview.”

She argued she had done nothing wrong and that the mistake was “inadvertent and Freudian” as she tries “really hard not to misgender people”.

But on Wednesday Green pointed to a tweet sent by Farrow on 4 October last year, and subsequently deleted, which read: “What she did to her own son is illegal. She mutilated him by having him castrated and rendered sterile while he was still a child.” Farrow also accused Green of child abuse.

Farrow said: “I have pointed out to police that I am a Catholic journalist/commentator and it is my religious belief that a person cannot change sex.” She added that she would “happily do jail time” for her “right to say that people cannot change sex”.

Green and other activists for transgender rights view it as deeply offensive to deliberately use the wrong pronoun for a trans person. Doing so could be an offence under the Malicious Communications Act, which makes it a crime to send messages that are indecent or grossly offensive, threatening, or contain information which is false or believed to be false, if the purpose for sending it is to cause distress or anxiety.

Police said for a complaint to be dropped, a withdrawal statement must be made. It is understood that has not yet happened in this case.

Breaking the law carries a maximum sentence of two years in prison. Farrow said the police’s decision to launch an investigation was an “outrage”. She tweeted: “I can’t sleep I am so furious.”

Responding to the controversy over the case on Wednesday, Green said: “Every day, people misgender my daughter online, that wasn’t uncommon. What was uncommon was that this was a journalist who had a public platform, who used that to send very malicious and nasty messages.”

She went on: “It’s not just the misgendering, it’s actually the context that she puts it into and that she calls me a child abuser … it’s also the stuff around mutilation and castration. It was the really damaging things she said about me.”

Asked if she believed alleged hate crime is an urgent life-or-death matter, Green told the BBC: “I don’t think that any hate should stand and I also think that the damage done by online communications is absolutely immense.

“And to say that this is not as important as other things – well, the police need to make those decisions, the CPS make those decisions, I don’t.”

A statement issued on the Mermaids website on Wednesday added: “The tweets are a lot more serious than about misgendering. They were allegations of serious misconduct and vile and spiteful personal attacks. The content was not about misgendering and it is unfortunate that so much of the media has fallen for the incorrect claim that they were.”

Surrey police confirmed on Tuesday they received an allegation over tweets by Farrow on 15 October. A police spokesman told the Daily Telegraph: “A thorough investigation is being carried out to establish whether any criminal offences have taken place.”