The word child is not a plural pronoun. It is a noun. Here we are speaking of one child. There is nothing plural about a child.
You should have been an English teacher.One type is a plural pronoun, a pronoun that refers to and takes the place of plural nouns (a noun that refers to more than one person, place, or thing). Some common plural pronouns are them, they, their, and us.
TheThat is a singular noun. The use of the word they or them is grammatically correct when the predicate is singular.child in question is eligible for driver's education. The mother does not want the child to get their license as soon as they are able to (age 16),
I'm not commenting on OP's use of the words them and they which are plural pronouns.
I think it is clear that we are speaking about one child.
They/them is frequently used as a gender-neutral pronoun.
Second, "they" and "them" are sometimes used to refer to a single person whose gender is unknown, but "they" and "them" are not "gender-neutral" singular pronouns. The only singular, gender-neutral, third-person pronoun in the English language is "it."
Third, if a parent (or person acting on behalf of a parent, as the OP appears to be) is referring to a single child, he/she will typically refer to the child as "he" or "she" (or "him" or "her"). I have never before seen a parent refer to a single child as "they" or "them."
Thanks for all of your responses. Well, except for the English lessons. This is an informal Internet forum, not a peer-reviewed medical journal.
It sounds like the best advice for the mother is to not sign or pay for anything. She should just let the father do whatever he wishes to do regarding getting the son a vehicle, license and insurance.