Well divorce has nothing to do with this "conversation" we are having in this thread, so that's one thing.
"Depriving them of everything they want is part of parenting..." is the real nonsense. That's how children learn to resent their parents, and in extreme cases, hate their parents. That's where the aforementioned communication plays a big role. Depriving them for deprivation's sake, because they don't know what they want, is an abysmal parenting technique. Authoritarian parenting is proven to be one of the least effective styles of parenting in developing grounded, happy children.
In many ways, a 4-5 year old knows what they feel better than a 7-11 year old child, or an adolescent, or a young adult. When you are 4-5, you have not developed the capability to lie convincingly. Things are black and white to young children. The research is still in early stages, but it's not as if a boy is saying, "I like to wear dresses and play with dolls." He will say, "I am a girl."
I know that it won't convince you in any way, shape, or form. But, still felt like someone had to try to set the record straight.