Logical Fallacy

Like the mistake "If there's smoke, there must be fire." your deduction of eliminating possibilities isn't as much of a problem as it is to then formulate a 'therefore' based on an arbitrarily concocted list of solutions.

Some may know this as the "god of the gaps" fallacy otherwise known as the Argument from Ignorance. Based only on what you know to be false, you cannot derive any conclusion about what it is. You're missing the step where you also try to rule out your conclusion in the case it is false. If true, you should be able to try to conclude it to also be false and find that you are unable to finally do so.

Science is the art of trying to prove something to be false and keeping only that which you're unable to prove false. That doesn't guarantee truth, nothing besides mathematical proofs can do so. It just leads you closer and closer to truth the more you rule out that which has shown to be false.

This is a False Dilemma , which can more than 2 choices presented, like in this case.

This would be a False Trilemma Fallacy, which is just an add on to the False Dilemma  Fallacy since there are more than just two options given in this example.