I am also going by something that you may be unaware of. Many adults start with an attitude that goes something like this:
I don't have a right to be doing this. It is not my place, and I am ridiculous. The poor playing which I myself can hear proves that I have no talent, and as soon as my teacher sees this he will hate teaching me. In fact, he is probably teaching me out of pity or for the money. There is something wrong with me: my age means that I learn very slowly, forget things, my body is brittle and can't do much. I know this because everyone says so. I'm already doomed.
You take this mindset, and continually tell this person that he can never (whatever) - it's the worst possible thing.
What you do do is explain how learning works. You explain that being able to play notes evenly is a huge and important thing. You explain that being able to count to four and play in time is a huge thing, it is in fact difficult, that the foundation of the greatest players lies in such abilities. You explain that what will impress you at this time is that if you ask for even playing, and it's practised, and the student comes back with it, that this is what will please you the most, because it means you are both building that foundation.
You do away with misconceptions. You understand those misconceptions, the emotions that they cause, and get at them from the core. You do not address the side effects of the misconceptions. So many times teachers talk about adult students trying to impress them, when in fact that student may be desperate not to be dropped because he does not understand what the criteria actually are. He does not understand how it works. Instead of explaining how it works, they go at it with "You will never become a performer." because they don't know what is going on. They address the wrong thing.