What’s wrong with this sentence?

What’s wrong with this sentence?  (Beware.  This is a trick question.)

Your child should wear a good pair of sneakers so that they may participate in PE.

Okay, here’s the answer:  Aside from the blatant grammatical error, what’s really wrong with this sentence is that a teacher wrote it.  How in the world can you believe the local teachers are capable of educating your child when they’re incapable of writing a simple, correct sentence?  I’d like to be shocked.  I’m just saddened.

(By the way, if the teacher is afraid of sexism by using “he”, or afraid of awkwardness by using “he or she,” the sentence could be redrafted to read “All children should wear….”)