Question

why is there both H- and H+?

Answer 1

Since hydogen has a nuclear charge of only +1, its one valence electron isn't held all that tightly, and since it achieves a closed-shell configuration (equivalent to He) by adding an electron, adding an electron is also not that hard.

In fact, hydrogen forms the +1 cation much less readily than most elements from the left side of the Table -- certainly much less easily than the other Group 1A elements -- it does not form ionic compounds with nonmetals, but rather covalent compounds it which it has an oxidation of +1. Even the "H+" we discuss in solutions of acid is actually present as the H3O+ molecule.

Hydrogen acquires another electron about as easily as other Group 7A elements, so that it does in fact form ionic compounds with active metals in which it exists as the -1 anion.