Turning a thing done for pleasure into a requirement is a great way to make the thing no longer pleasurable.
In your place, I would explain why the school has such a program... so students who are not interested in books will have a chance to become interested, and so students who are at or below grade level in language arts will have literature that helps them improve.
And then I'd say, since you're neither of those things, that's why you're not going to participate anymore.
Finally, I would ask the teacher if it was okay for us to waive the entire reading log idea for my DD. If not, I'd simply fake it all year, randomly changing titles whether DD had read them or not.
My DD has a 20-minute-a-night requirement, but does not have a log, so I don't have this issue. Her G/T class has been assigning reading projects, but at least she gets to choose her material, and she's been pretty happy with her choices so far.
