If I cast Inquisition of Kozilek, and my only target is a Loxodon Smiter, do I have to make my opponent discard the Loxodon Smiter, or can I "fail to find" just as I would if i were searching my library?
You can "fail to find" a card, but only while explicitly searching someone's library or hand. In the case of Inquisition of Kozilek, you are not "searching" the zone, so you must choose a card if a valid choice is available.
Per the comp rules, "fail to find" is specific to searching a hidden zone:
701.18b If a player is searching a hidden zone for cards with a stated quality, such as a card with a certain card type or color, that player isn’t required to find some or all of those cards even if they’re present in that zone.
While the hand is still considered a hidden zone even when it is revealed (CR 400.2: "Library and hand are hidden zones, even if all the cards in one such zone happen to be revealed"), Inquisition of Kozilek's instructions say to choose a card from it, not search for one. Thus, you must follow the normal rules: which is to carry out as much of the actions as possible.
So, you may still be wondering: why doesn't this rule come with a "fail to find" clause?
The simplest explanation is that it's part of the underlying logic of the Magic comp rules — to minimize actions that players can't "double-check" using public information. (Consider the difference between Vampiric Tutor and Mystical Tutor, for instance. What purpose does the extra "reveal" clause serve?)
Adding "fail to find" to the rules for searching guarantees that your search will result in a valid game state without forcing you to prove there are no valid choices by revealing your entire library.
Inquisition of Kozilek doesn't need a "fail to find" rule because it says "reveal" — all players get to see the targeted players' hand and verify whether there are any suitable cards in it.
If a discard spell said "Look at target layer's hand" instead of "Reveal," the rules manager would probably insist they include a "may" clause, like Vendilion Clique.