I have a library. It is set to anonymous access. But when I broke the inheritance on a single page in that library, the anonymous access was gone. Is there a way that I can break the permission inheritance of each page and still keep anonymous access?

My final goal is to make all pages in a library anonymously viewable. some pages are only editable by the owner and some pages are only editable by the contributors.

Nope, what you have experienced is by design. I've got a blog post on how to exempt an individual page from anonymous access and what you describe is exactly how to do it. Anonymous access is only handled at the Web or List/Library level. There is no way to set it at the individual item level. A more detailed explanation can be found here: http://www.dontpapanic.com/blog/?p=12Paul Stork SharePoint Server MVP