Initially I thought that `expectation_format_method` was only set to a value once -- where it's set to `to_not` below.  I was trying to figure out where it got set to `to`.  I didn't see it because you made it a default arg.  I think making it a default arg is OK if any callers of this method actually pass a value -- but otherwise it's confusing (and easy to miss) to have it be a default arg like this.

Actually, why not make it an ivar and then `does_not_match?` can set it to `not_to`?  Then you don't have to branch on it here.