Being forced to publish a paper?
My first guess is that you think your work is worse than it really is. This is a variation on Imposter Syndrome of course. The director, however, knows your work and presumably something about the field. His faith is stronger than yours. 

But to ease your fears, I'd suggest that you try to work with the director to refine your paper. Along the way you can bring up your reservations naturally and, probably, address them. If you can arrange this, then you might include the director as co-author, depending on the degree of collaboration. 

Even if your paper isn't perfect (few are), you probably have something valuable to contribute as the director indicates. Indeed, the methodology of the paper might be much more important to the community than the immediate results. 

Also, I hope that the publication system of the journal includes good reviewers. By submitting it you will get additional feedback from knowledgeable people that will help you improve the paper before final publication. Even without the director's direct help, the review should be valuable. 

Publishing just seems like a big win to me.