Strength identification in conjugate acid-base pairing I'm a student in highschool AP chemistry. I'm confused about a certain problem in my chem textbook. In summary, I am given a species and asked to identify its basicity as strong, weak, or negligible. I must then give its conjugate acid and identify likewise for its acidity. (in the context of Brønsted-Lowry theory)

I understood all parts of the problem except for $\mbox{O}^{2-}$, to which I assigned the conjugate acid as $\mbox{OH}^{-}$. It was correct thus far. My guess that they were both weak was wrong, however. According to the solutions page, they're both strong!

How is $\mbox{O}^{2-}$ a strong base? How is $\mbox{OH}^{-}$ a strong acid? To my knowledge, neither are found in the canonical strong acid/base lists, and neither seem to satisfy the "completely ionize in water" definition.
$\ce{H2O}$ is a weak acid.  Abstract a proton to give $\ce{HO^{-}}$, a strong base.  Abstract a proton from that to give $\ce{O^{2-}}$, a very strong base.  See a species as a whole, up and down for a property.  

Try it with ammonia.  Feel free to wonder why $\ce{Li3N}$ is red.  Look what a very strong base can do,

$\ce{Li3N + 2 H2 → LiNH2 + 2 LiH}$ (reversible at 270°C)