How can a two year old be pronouncing his want to be a boy? That doesn't happen out of nowhere? Most kids don't speculate much in terms of gender roles, they're just children.
I think the parents would have some idea about that, who am I or you to insist on something other than their experience? Yes most are just children and don't care (because their gender identity lines up with their sex, it's not necessary to, you and I never went through that because we are not transgendered). But like the dr said in the video, these things do and can happen very young for the minority of people in this world who are transsexual.