English doesn’t have “grammatical” gender at all, not even for he, she, or it. The “gender” he, she, and it refer to the actual, real-world gender of the antecedent, not its grammatical gender. In general, one would use the word she for child because this particular child is female.
Even in cases such as this, where there is no actual person (or there are several people, in a mix of genders, and the text is referring to any one), the language still refers to the hypothetical “example person” as a person, with a gender. The pronouns used, therefore, reflect the gender of the example person. Again, this is not grammatical gender.
In the past, as a matter of convention, “the example person” was always male, and thus he was used as a pronoun for the example person. More recently, the example person will sometimes be written as female, that is, with she. Some authors will also use both roughly equally (though they can only switch when introducing a new example person; for clarity, any person who is supposed to be some consistent example individual could not switch genders).
The reason for this is simple: by having the example person consistently be male, you give the impression that all of the people involved are male. It has not always been clear when male was chosen by convention, or because the individual under discussion actually is expected to be male. Switching to female does not fix the ambiguity, but at least it makes things more even: by having everything use male examples, it gives the impression that men do everything.
Finally, it is not gender-neutral, it is the gender-specific pronoun for the neuter gender, that is, the gender of inanimate objects. It is almost-always inappropriate, if not exceedingly offensive, to refer to a person with it as it implies that he or she is not a person, or not even a living thing.