I'm not sure there is a precise name for the full construction. But that is a
non sequitur. Non Sequitur is anywhere when it "does not follow". So you could just respond with "that's a non-sequitur".
It also reminds me of the god-of-gaps fallacy, where whenever there's something science cannon explain, then that's where a god is, in the gaps of science. That's an "
argument from ignorance"
And closer to your example, the
argument from silence.
But I think the non sequitur is best. Unless he actually explains why it follows that your inability to offer an alternative explanation proves his explanation to be true, then it does not follow.
You can also nullify it somewhat by noting there are several possibilities, some of which seem more likely than others, but you can't be sure what the answer is. That leave open the possibility that his answer might be correct, but then he has to explain why it's more probably than other answers. I don't know 100% what that white line is, but why are chemtrails more probably than contrails? I don't know why you are hearing voices, but why are government microwaves more likely than auditory hallucinations?