What can I do if my professor says he won't let me publish my biology research?
It is true that sometimes people may just search for pretext and will give all shorts of excuses. However, before jumping to that conclusion you should ask yourself are you sure you are right? Most of the times professors will actually give proper advice within the limits of their own personality and human nature.

So to answer your question try to examine and verify that your work is up to the expectations of your supervisor.