Why are alkali hydrides strong reducing agents?
Just like I said in the answer to you broader question, it's all about elements and their individual preferences. Hydrides (of any metals, not necessarily alkaline) contain hydride ion $\ce{H-}$, which is basically a hydrogen having one extra electron (or, in other words, a hydrogen in oxidation state -1). Now, hydrogen's electronegativity is relatively low for a non-metal, and so is its electron affinity. It can be said that hydrogen takes that extra electron almost reluctantly, and is ready to give it away to any oxidizer, even a weak one. This makes the hydride ion (and any compound which it is a part of) a powerful reducing agent.

In due time you will learn about the redox potentials which are a quantitative measure of the compound's oxidizing or reducing power. (Yes, they may depend on temperature and other things.) I'd rather not touch on that right now, for it's a long story.