I can't believe that in five years she never asked....

She thought he was a teacher, I believe, so she must have made incorrect assumptions from something he wrote and he never corrected her. There's a scene later in Ireland, after she's discovered that he's a priest, where she tells her young friend Janet that he does his teaching from the pulpit!

But yes, it's odd, even if she had incorrectly assumed he was a teacher, that during all those years of correspondence she never asked him what school he taught in or what age level or subject, or never found it strange that he never shared any school tales of his students or fellow teachers.