Based on his Press Release, why would President Truman be against sharing the secret of the atomic bomb with the world?
I tend to think that the fundamental reason that President Truman is against public disclosure of atomic technology because he wasn't quite sure what he had. The emergence of atomic technology as a viable nuclear weaponry threat was transformational in how the United States would emerge as a superpower and how other nations would interact with it. Truman recognizes this and also recognizes that in public disclosure, he and his government no longer control atomic energy. Rather, they are controlled by it. In the interest of carving out a foreign and defense policy with the presence of nuclear weaponry technology in mind, Truman states that while it is not national policy to keep such elements in secret, it does make sense for the United States to not share what it knows about what it has. I think that President Truman does tip his hand a bit when he makes clear that the United States possesses something that is quite intense and will transform the landscape of the world:
... pending further examination and possible methods of protecting us and the rest of the world from the danger of sudden destruction.
President Truman feels compelled to be silent about the capacity of what he has simply because he lacks full understanding of what it is, but knows enough to know its destructive quality and "sudden" capacity for danger.