There is a 2020 study that showed that 80% of Transgendered individuals have considered suicide and 40% have attempted it. So reducing those rates by 50% or more is substantial numbers.There is no worse outcome than suicide. But what if the suicide chance went from 1% to 2% when parents don’t play along (100% increase!) but the other 98-99% of the time the kid turns out to have a way better life? This example is just illustrative. Point is suicide stats alone don’t tell the full story without the context of what the outcomes are for the vast majority of people.
There’s also a middle ground where you can support your child and try to be there for them but still not accept the idea of being transgender. A good analogy in my mind is the same way you’d respond to someone you love being an alcoholic. I use this example because there is alcoholism in my extended family. To support an alcoholic you don’t just encourage them to drink just because that’s what they have an urge to do. You empathize with them, you support them however you can as they seek help, and you’re there as a trusted confidant for them. You don’t abandon them if they fall off the wagon a time or two. But the ultimate goal is to show you love them as they try and work through it all.
And again, you still haven't identified what you think the harm of calling someone by their preferred name and pronouns. What are these bad "average life outcomes"? I genuinely don't know what you are concerned about happening to these kids.
If I had to guess, you may be concerned that if you call these kids by their preferred name and pronouns, then they will continue to be transgender. But that concern only holds water if there were some evidence that refusing to use the name/pronouns convinces them that they are not transgender. And there is Zero evidence that this is true. The only outcome of not using these terms that is supported by peer reviewed evidence is a substantially increased risk of suicide. I don't see how any other outcome, particularly when not backed by any scientific evidence, could outweigh that.
The psychological benefits of using their preferred name and pronouns accrue to the individual even if you don't agree that it is legitimate. Why would you not do something like that?