Two Solutions to the Pronoun Gender vs. Pronoun Number Agreement Conflict

Generalize in the Plural:

Students who . . . they . . .

Grammarians ought to . . . or they would not bother trying to . . .

Or Generalize in the Singular to the Only Possible Gender:

An NFL quarterback should always . . . because he . . .

A member of Goucher's Women's Field Hockey Team never . . . although she sometimes . . .