I only agree to write a reference letter if I can write a positive one. Although it is only hypothetical at this point, I would hesitate to write a reference letter for an individual who chooses not to waive their right to see it. That said, I have sometimes shown students my letters for them since I feel it is useful for them to know what I have written. It also provides them a chance to remind me of things I may have forgotten. I do not do this consistently, but am considering making it a personal policy.
I guess I have two questions. Is there a reason not to show a student their letter of reference? Just to be clear, this is for a letter I have written for the student and not for a reference I have recieved. The second question is, is it reasonable to refuse to write a reference for a student when the student does not waive their right to see the reference.
Yes, that's two questions.
Yes, you can and should decline to write a reference letter if the student does not waive his right to see it because the receiving institution will discount the letter and it will be a waste of your time.
Since you should never write a bad reference letter (you should decline instead) there is no reason not to provide a copy to the student. Tell them to be cool about having received the copy.
Here is what I tell students: http://ksuweb.kennesaw.edu/faculty/rbrow211/recommendations/index.html#waiver