Which is basically what the NYT said in their response:
"We received the letter from GLAAD and welcome their feedback. We understand how GLAAD sees our coverage. But at the same time, we recognize that GLAAD's advocacy mission and The Times's journalistic mission are different.
"As a news organization, we pursue independent reporting on transgender issues that include profiling groundbreakers in the movement, challenges and prejudice faced by the community, and how society is grappling with debates about care.
"The very news stories criticized by GLAAD in their letter reported deeply and empathetically on issues of care and well-being for trans teens and adults. Our journalism strives to explore, interrogate and reflect the experiences, ideas and debates in society - to help readers understand them. Our reporting did exactly that and we're proud of it."
The only right alleged is a right to exclude trans women, and consequentially a right to screen all women suspected of being trans.
> and the medical abuse of children
The children in question want to transition, and their parents or the state want to prevent them; defining this as "abuse" without actually listening to the allegedly abused is the problem.