Evidently, the poster's creator thought he/she would have looked or read awkwardly, and was trying to skirt the gender issue.
English has a few different ways to deal with this problem. Besides he/she, you could simply choose he or she (though some might feel that choosing one or the other makes the quote seem exclusionary):
When you show the moon to a child, she only sees your finger.
Other times, the singular they is used. (Some grammatical purists might disapprove, but such disapproval seems to be waning):
When you show the moon to a child, they only see your finger.
You could use the child, but some might find the repetition a bit clunky:
When you show the moon to a child, the child only sees your finger.
Another way to address this is to pluralize child, and thus use the more gender-neutral they:
When you show the moon to children, they only see your finger.
Faced with these alternatives (all of which have pros and cons), the writer opted to use it.
Is that acceptable English? I found this statement in an answer on ELU:
I'm afraid it would be wrong. You should never use it to refer to people, except perhaps when the word you are referring to is child and its sex unknown.
Wikipedia says:
The word and term 'it' can be used for either a subject or an object in a sentence and can describe any physical or psychological subject and/or object. The genitive form its has been used to refer to human babies and animals, although with the passage of time this usage has come to be considered too impersonal in the case of babies, as it may be thought to demean a conscious being to the status of a mere object.
Grammatically, I suppose using it might be deemed acceptable (since we are dealing with a child of unknown gender), but its usage would at least raise some eyebrows. Had I made the poster, I probably would have used this version:
When you show the moon to a child, the child only sees your finger.