I just wrapped up a really great conversation with the head of the history department that didn't hire me. (For the sake of pseudonymity, I'll keep the school to myself, but to whoever got the job: You got the gold ring, my friend.)
As the chair and I discussed my interview, it became pretty clear that my candidacy was doomed by two things: rookie mistakes and Baby Tiger Syndrome.
The rookie mistakes I made came in the teaching demo, and in conversations with administrators. My teaching mistake is that I came in to the class as if it were the middle of the semester rather than the first day. I'm a big, loud guy. I pace the classroom rather than stay at the podium, and when I get excited I exhibit mannerisms that look a bit like a minor seizure. By the end of the semester, my students are used to my shtick, and find it quirky and endearing. They also figure out that I raise my voice when they are right, not when they are wrong. But on Day One (and on the interview there is only Day One), it's weird and unsettling. Moral of the story: Don't unnerve the students. You're used to walking into a room full of strangers, they are not used to a stranger walking in and scaring them. If you are soft-spoken, or project warmth, no problem. If you project "tough" rather than "love", throttle back a bit.
My second mistake was in answering the question, "Why do you want to leave the tenure-track?" This is really important: They do not want to know why you want to leave the tenure track. They want to know why you are interested in teaching at their school. When they asked my why I wanted to leave Underfunded Third-Tier State University. I told them: The teaching environment sucks. My students can't/won't read. "Student Success" means not failing anyone. The humanities are treated as an inconvenience by studetns and administrators alike.
Big mistake. In my case this raised the question of whether I wanted to work at a prep school, of if I was just trying to get the hell out of Dodge. Moral of the story: "There are a lot of great things about my current job! I really like my colleagues and the department majors are wonderful. It's just not the right fit. Your school is." I'm not saying you should lie, but be aware that prep schools are unsure why anyone would want to leave the tenure track (ha!). If you don't make the case for the benefits you see in teaching at a prep school environment, you will crash and burn as I did.
This leads quite nicely to Baby Tiger Syndrome, which is defined over on Worst Professor's blog. As the Chair explained during our conversation, an administrator who is risk averse is not inclined to hire a PhD. There are going to be lots of very good candidates who can do the job, and will go twenty years without causing a problem. Simply by virtue of having a PhD, and even more if you are on the tenure-track, you do not fall into that "Safe" category. You could be a tremendous hire, to be sure, and they may say, "That's our next Head of the Upper School." But the chances are that for you to get a job, someone is going to have to take a chance. It is your job to minimize the perceived risk in hiring you. How you do that is up to you, but it's probably pretty closely linked to the rookie mistakes described above.
But what the hell do I know? I'm 0-for-Life on the prep school market.
Good luck, us!