~Ohios,
The short answer is that the Unless Equation always works. The Unless Equation diagrams the statement as a conditional. Your question then asks why the reverse doesn't work, and the answer is that the reversals are Mistaken Reversals of the conditional. For those reversals to be acceptable, the original statement would have to be a biconditional. And the Unless Equation says it's not. Even shorter: trust the Unless Equation! It's always right.
The longer answer involves what "unless" means in natural language. "B reads fourth unless C reads fifth" means something like "B must always read fourth, except when C reads fifth, in which we don't care and B can be anywhere that's otherwise acceptable." You're instead reading the statement something like the following: "B reads fourth, except when C reads fifth, in which case B can't be fourth." That's not what it's saying; it's not what "unless" means.
An example: "I'll start reading this book unless the phone rings." We would diagram:
read 
rings
And:
rings read
Given my original statement, I have to read the book if the phone doesn't ring. But if the phone
does ring, I'm still allowed to read the book (and not have made a false statement with my conditional). The statement is essentially saying that I must read the book, although there is one situation where it's optional: when the phone rings. So if the phone doesn't ring, the one situation that would allow me not to read the book is false, so I must read it. If the phone does ring, there's no compulsion at all, and I can read or not read, consistently with my original statement.
If that weren't a correct analysis of "unless", then the Unless Equation would never work. The analysis is fine, but too time-consuming on a real test! So let me bring it back to the beginning: trust the Unless Equation.
Robert Carroll
