What should we use as gender-neutral pronouns for non-binary people?

It is improper grammar to use singular "they/them"

Question: What should we use as gender-neutral pronouns for non-binary people?
Position‹2 of 3›: We should use a new set of gender-neutral pronouns for non-binary persons
Argument1 of 2›: It is improper grammar to use singular "they/them"

It would be detrimental to learning to change the grammatical rules which are already in place, as students would then have to unlearn old grammar - it is more difficult to unlearn something than it is to learn something new. Therefore it is more logical to use a new set of gender-neutral pronouns.

The argument

"They/them" is plural and that is that. To suddenly change a fundamental part of the foundation of grammar would be confusing to students and to grammarians everywhere; and if the teacher is confused, then how are the students supposed to learn?

Premises

[P1]"They/them" is grammatically plural. [P2] Suddenly using it as a singular pronoun would confuse students and grammarians by altering a foundation of grammar. [P3] If even the teacher is confused, students cannot be expected to learn it. [C] Therefore, because it is improper grammar to use a singular "they/them," we should use a new set of gender-neutral pronouns for non-binary people.

Counter-arguments

Singular "they/them" is gaining acceptance within many scholarly circles and has already been in use for decades, and was previously in use centuries ago. It is actually the plural-only usage of the pronouns which has upset the grammatical balance. This is only an example of how language changes over time. Singular "they/them" is already a part of the natural evolution of the English language, and the change should be embraced, not stonewalled.

Rejecting the premises

[Rejecting P1] Singular "they/them" is becoming more and more accepted by society and grammarians.