I am fairly certain that the success rate of converting people with these visits is very low. But, they do it anyway, usually with young members, and usually in pairs. Why is that?
I suspect these visits have more to do with re-affirming the young members' commitment to the church, and it is less about any actual desire to convert people.
Issuing a challenge like this is part of that process. Because, any answer you give: They will most likely reject or wave off. Then that allows them to re-affirm their faith, because you could not beat their challenge.
Any "whoppers" you think you might have, such as the examples in this thread, are NOT likely to work, either. They can wave them off, or get an official answer from the Church that they can accept.
Assuming my hypothesis is true: If you genuinely wish to help them learn something, the best bet is to undermine the re-affirmation process, before it has a chance to happen.
To do that, do NOT answer their challenge directly. Instead, start with the diplomatic approach that I outlined in my previous post, here.
Tell them the challenge is unnecessarily combative. Inform them that both sides could live in peace and harmony, and mutual tolerance for each other. You can respect their faith, as long as they respect your lack of it.
Do NOT try to convince them that Mormonism is "wrong". Focus on positive traits on what you think is a better state of mind. Let the values of your own ideas stand on their own merits, instead of trying to take theirs down.
For example: I would tell them that I found a devotion to empirical results to be more reliable, for my own needs. Appeals to scripture and authority are certainly not going to change that for me. Because, I find value in having authorities challenged on occasion.
But, as long as they remain nice people, they can follow their books as much as they please. The only "wrong" people are the jerks: those who are mean, nasty, and violent towards other people, regardless of whether they are religiously faithful or not.
You could even, gently, inform them that their challenge perhaps inadvertently made them seem like jerks to lots of people. It was NOT their intention to be jerks, for sure, but if they really wish to be pleasant people, they would be better off not trying to spread their ideas to others, in this door-to-door manner.
And, perhaps if they stick around long enough, perhaps you can even go into my hypothesis with them: You could, eventually, tell them that you suspect this challenge isn't really about conversion, but about confirming the faith of the challenger. They probably won't agree, at first. But, if you point out the evidence that makes you suspicious of this, perhaps it will give them a little something to think about. If you do it carefully, enough, anyway.
You might not have beaten their challenge, directly, but you would undermine the whole reason they issued it, in the first place. Which, in my opinion, is an even better victory!
