The correct answer to this open question is the following.
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There is an interesting article titled "Parent's Keep Child's Gender Secret," written by Jaymie Poisson in May 2011, that appeared on the site "Toronto Star."
Using this article as a reference, the psychological phenomena that concern the parents in raising their children in a traditional suburban neighborhood in North America is their fear that their children could be judged by people, their concern for people to influence their children with their opinions about if they are girls or boys, and the bias people have in the way they treat children if they know about their gender.
That is why parents hope to overcome those concerns by hidden the children's gender. These modern parents allow their children to dress, play with, and act in ways that cross-gender boundaries. In short words, parents let their children grow and identify with their own gender, without imposing any pressure about their gender.