Post History

Well, your teachers were talking rot, as they often do. Though, to be fair, the aim of their teaching was probably not give your the full art of writing, but simply to introduce a little elementary structure into the chaotic way many people communicate.

But in the passage you cite, the author does explain why you might introduce new material in the final paragraph. The final paragraph can be used to sum up the argument of the piece, but it can also be used to point onward and outward, to provide a pointer to what comes next. 

Thus if the essay has provided a practical solution to an immediate problem, the final paragraph might say, but if you want to understand why this solution works, and so you can solve similar problems in the future, you may want to learn the theory behind this. 

Another example might be an essay that argues a point of law to prove what the law actually says in a particular case, but then, in the final paragraph, it might advocate for a change in the law. 

These "what next" examples do not belong earlier in the piece. The body of the essay is concerned with the current question -- solving the immediate problem, clarifying the current law -- but at the end it can make good sense to point the reader beyond the immediate, to the principle on which the solution is based, or to a change in the law that might make it more just.