Perhaps I'm just neurotic, but I do find it uncomfortable to write code with someone scrutinizing my work. When figuring out how to implement an efficient algorithm, I find that it's often helpful to perform exploratory steps before actually writing the algorithm. For instance, when I attempt a projecteuler puzzle that I don't immediately know the solution to, I'll usually try to compute the desired result for a few simple inputs, or I'll quickly write down the first (naive) approach that comes to mind and then trace through it to see where it fails, etc.

I know that those are all things that I can still do during a whiteboard interview, but having the interviewer look at my intermediate work, assume that I'm making mistakes and try to correct me tends to disrupt the process. I'm confident that the algorithms that I'll ultimately produce will be good, and I'm confident that I'll produce them at a good speed, but it will still look worse to the interviewer if I write down a bunch of noise before outputting a polished algorithm.

On the other hand, on paper, I can quickly churn through some of those early steps and then show the interviewer a solid, finished product without them having to see the crude intermediate steps. Again, it's possible that my anxiety about this isn't really justified, but I can't help but get the feeling that working in this way will leave the interviewer with a worse impression of my abilities than if I have the option to "hide" the rough work and just show them the output.