The machine doesn't give you a choice: You have to cast it, if possible. However, there aren't any enchantments, nor any other artifacts, on the battlefield. However, you really don't want to destroy the machine, because you like it.
Question: Could you choose to cast the Tear half (ie. "destroy target enchantment"), have it fail because of a lack of legal targets, and have the card remain in exile?
A few clarifications for those readers who are unsure how Omen Machine (and such similar effects instructing players to cast a card) works: When an effect instructs a player to cast a card ("if able"), and there is no word "may", that means that the player has no choice, and is forced to cast the card, if it can be legally cast. For example, if the card had been a Doom Blade, and you are the only player who controls a non-black creature, you would be forced to cast it targeting your own creature. You can't choose to not cast it (nor can you choose an illegal target for it.)
However, if there are no non-black creatures on the battlefield, in that case Doom Blade cannot be legally cast (because there is no legal target for it). In that case the card is not cast and simply remains where it is (which in the case of Omen Machine is the exile zone.)
With a card like Wear // Tear, however, the situation is a bit more complex. When the effect instructs you to cast a split card, you have to choose one of the sides to cast (fusing is not an option because that can be done only when casting from your hand; here we are casting from exile.) Perhaps you could simply choose the Tear half, and then have it fail to be legally cast (because there are no legal targets for it) and have it remain in exile?
However, the correct answer is that if there are no enchantments on the battlefield, you have to choose the Wear half. Choosing the Tear part is not an option. The reason for this is a bit complicated, though. There is no direct rule in the Comprehensive Rules that states this, and instead it has to be inferred more indirectly.
We have to start by pointing out that in this situation casting Wear // Tear is an "effect", as per (the relevant part of) rule 609.1:
609.1. An effect is something that happens in the game as a result of a spell or ability.Anything that happens as a result of a spell or (as in this case) ability is an "effect". This includes casting a card, if it's the ability that's instructing a player to do so.
Rule 608.2d, in turn, states (emphasis mine):
608.2d If an effect of a spell or ability offers any choices other than choices already made as part of casting the spell, activating the ability, or otherwise putting the spell or ability on the stack, the player announces these while applying the effect. The player can’t choose an option that’s illegal or impossible, with the exception that having a library with no cards in it doesn’t make drawing a card an impossible action (see rule 120.3).Although it might be completely trivial and unnecessary to state, which half of a split card to cast is a choice (made during the casting process). For completeness sake:
708.3. A player chooses which half of a split card he or she is casting before putting it onto the stack.Part of the process of casting a spell is to check if can be legally cast:
601.2e The game checks to see if the proposed spell can legally be cast. If the proposed spell is illegal, the game returns to the moment before the casting of that spell was proposed (see rule 720, “Handling Illegal Actions”).Since the choice of half was what made the casting illegal, it's an invalid choice, prohibited by rule 608.2d above. The player has to make a choice that makes casting the card legal, if possible. In this situation choosing the Wear part makes casting the card legal, and thus that choice is mandatory.
