It can't, a board can contain many projects.
The project default is the last project the user was active in (although I'm not 100% sure of the actual calculation of "active" beyond "the last project they created or edited an issue in" - it's not always that, so I know I'm missing some of the rules)
Thanks... For any Atlassian reading that would ask why I need such a feature request:
We have a project that is the primary or front line project if you will. Our staff submits issues here, which is then fielded by our Knowledge Management (KM) department. Then KM either resolves the ticket or moves it into a new project if it's a feature request. When we communicate to the users via the new project they respond. After that point if they Create a new issue the Project field's value changes to the new project. A lot of times they forget to reset the Project back to the front line project even though we've trained them. So that's why it would be nice to have that be default.
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