You must create a Facebook Application using a personal profile. Since anyone can create a business Page, and at that, unlimited amounts of Pages, Facebook doesn't allow those Pages to also create applications. The reason is that they (Facebook) wants to know the person behind the Application in case there are issues. If Pages can create them, it's an added layer of obscurity as to who the real owner is.
With that said, once you create a Facebook Application, the user/profile of the creator is not displayed. It's only visible to Facebook as to who created the Application, so your users will not 'see' you as the owner.
Hope that helps explain,
Alex
JFBConnect setup
