"Why do I have to write the word down? Why can't you just read my mind?"
I'm going to tell you how I handle questions like these. Or, more accurately, how I used to handle questions like these. Since I rarely use a presentation as straightforward as "I'm going to read your mind," these types of challenges come at me less frequently. If, for example, a Ouija board is going to reveal the word they're thinking of, then writing down the word and burning it is just part of the process. They can't really question the writing down of the word too much because it's not like I'm claiming this is my process, it's just the process that I learned.
The majority of what I do falls into that category these days. I'm demonstrating something other than pure mind-reading so the writing down of information becomes more justified. For example, The Donny Ackerman trick. I'm not reading their mind, I'm stopping time and opening up this piece of paper they hold in their hand. The trick doesn't make sense if they don't write it down.
But, I still do the occasional mind-reading bit, and here are my thoughts on these sort of questions/challenges.
The easiest way I've found to avoid this issue is to not mention mind-reading or anything like that until after the word is written down. Don't say, "I'm going to read your mind. Here, write down any word you can think of. Now give it to me. I'll put it in my wallet." You're giving them too many opportunities to think, "What does this have to do with mind-reading?"
Instead, get the logistics out of the way first. "I want you to write down any word you like on this card.... Ok, I don't want to see it. Let's put it away for now." Once the word is put away, or the picture is drawn and sealed in the envelope, or whatever other process needs to be done, then you go into the "I'm going to read your mind" business. I think this is better because nothing is ever actively incongruous. When they write the word, they don't know what's going to happen next so there's nothing to question there. And later when you say, "Now, you have a word in your mind, and you've committed to that word [small gesture to the wallet], and I'm going to try and read your mind," they may at that time feel like the writing of the word wasn't completely justified, but it's not something happening in the moment that they need to question. If they think it's incongruous, it's only retroactively incongruous, so it's much less likely to be questioned.
So that's my first recommendation. Don't bring up mentalism or mind-reading until after the logistics are complete.
My second recommendation is this: Don't directly justify why you had them write the word down. Unless they specifically ask you why, only indirectly suggest why you did it. For example, above I said, "You have your word in mind and you're committed to that word," as I gesture towards the wallet. That's an indirect justification. It's better than saying, "I'm going to have you write the word down. The reason I have you write the word down is so we all have proof that I really did read your mind. I don't want you to say I didn't when I did, or say I did when I didn't, just to be nice. And I'm going to put it in my wallet so I can't see it. And also so it's safe." I don't think justification with that level of detail sounds great. It would be like if you caught me looking in your medicine cabinet and I said, "Hey, do you have any floss?" That interaction would probably slide by. But if I instead said, "Hey, the reason I opened your medicine cabinet is because I wanted to see if you had floss. I have a popcorn kernel in my teeth and it's driving me crazy. That's why I wanted the floss. To get out that bit of popcorn kernel. The one I mentioned before. The one in my teeth. I know people keep their prescriptions in their medicine cabinet, but I wasn't paying attention to them. I was just looking for floss," you'd wonder what the hell I was up to.
This is a life tip as much as a magic one: The more effort you put into your justification before being questioned about it, the less likely your justification is to be believed.
But let's say you get to the end of the effect and they do question why they had to write down the word. At this point you're free to justify the action in the most direct and convincing way possible.
Here are two ways to handle it.
This first way has been my preferred method in the past.
They ask, "Can you read my mind without me writing something down?"
I first give them an analogy. "Hmm... not really. It's like asking, 'Can you hear one particular song playing if your radio is broadcasting all the frequencies at once?' I mean, yes, the song is in there, but it would be almost impossible to decipher until you tuned into a particular frequency. Your brain needs to be tuned into a frequency that I can pick up on too. So if I say, 'Think of the word you wrote down,' that's something definitive I can try and pick up on. But if I just say, 'Think of a random word,' there's almost no way of deciphering that because there is no substance to it. At any moment your mind is filled with random words to some extent. So writing the word down provides some focus."
I then do a bit of verbal jiu jitsu to take the question and flip the entire premise. "I know there are some people who claim to be able to read someone's thoughts without having them write it down or see the word in a book or something... but I think those people are faking it."
See? I've taken this act that they thought was questionable (writing the word down) and suggested it's an indication that what they're seeing is genuine.
Here's another alternative for justifying the writing.
They ask, "Can you read my mind without me writing something down?"
You answer, "It depends. Sometimes, maybe, for simple stuff. It's like... actually, I was just reading about this the other day. Let me see if I can find it. I saved the blog post because it definitely echoes my experience with this sort of thing."
You then pop out your phone or laptop and bring up the article you were reading that talks about a study showing how writing something down affects focus. You read one line from the article, "The act of writing not only 'boosts the signal' for the information that is written down, it also suppresses extraneous 'noise' from sensory input and memory."
The blog post about this bogus study is on the new DMB site that I mentioned last Friday. Look for the post called Writing and Memory on 9/20/17. It even has a line that helps justify ripping the paper in a center tear or putting a business card back in your wallet.
That post features this illustration by Iain Dunford which I think will help them visualize the (supposed) effect writing has on their focus.
The truth is, if you don't perform much, and this is a concern of yours, you can relax about it. Most people will never question you about these sorts of things. But even though that's the case, I think your presentation will be stronger and more assured if you know what you'll say should the subject come up. So have a plan, but there's no need to worry about it too much.