Dad seems to be heavily into “boys things and girls things”. The mother, I believe, is a paediatrician and has allegedly taken advice from two other paediatricians, the first of whom was not a “gender specialist”.
Having read the actual judgement delivered by the judge in this case (who overruled the jury), the father is not into reinforcing sex stereotypes but prefered a watchful waiting approach, the mother wished to adopt an affirmative approach.
In the US this would put the child on a medical pathway in line with current practice, starting with puberty suppressing hormones from around 9 years old and cross-sex hormones from around 12 years of age.
The father has come under criticism for going to the media with this and the judge imposed a gag order on both parents until their twin boys are 18 in response. I agree with those who say that this shouldn't happen when children are involved in these type of custody battles. However, the father believed this was the only way to protect his son from being affirmed as a girl and eventually medically transitioned.
The same judge had previously given the mother the exclusive power to decide on medical treatment, but has now clearly changed her mind on that.
Neither parent was in any way abusive or harming the child - this was emphasised in the judgement where she awarded joint custody to both parents as of 2020.
So this was a disagreement between two parents who both believed they were acting in the best interests of the child. And the judge has now decreed that the child cannot be affirmed as a girl unless the father agrees and that no decision on medical treatment can be made without both parents agreeing. If they cannot do so, the judge also appointed a mediator who would seek to help them agree and who if that was impossible would then make the decision for the parents.