OK, so I figured out (via checking the Pfhorums) what I was supposed to do.
There's this window-shaped indention on the right side of the demolition point. You have to tab the left side of this once, then run. Tab the right side first, and you're screwed--the left side will beep a few times, then pffht. You CAN apparently save before doing this, contrary to what one person there said, but it might have only worked for me because I reloaded.
So, uh. I guess this topic could serve as a how-to? Otherwise I'm clogging the forum with useless threads. :U