On the saying "Noone goes into teaching for the money."

The familiar saying "noone goes into teaching for the money" is an often repeated dictum given to would-be teachers, youths in college, and the like. I once heard the New York City Chancellor of Schools repeat this adage in an address in which he explained why the salaries of teachers were not higher than they were. We may reconstruct the former Chancellor's statement to mean something like, "one ought not to go into teaching for the money." Or, perhaps more forcefully, "everyone goes into teaching for none of the money".

So from (1.) "noone goes into the teaching for the money"
we infer (2.) "everyone goes into teaching for no money".
Now, this is a valid inference by obversion.

But by inferring 2 from 1 we see that 1 cannot be true because 2 cannot be true.
From the fact that "noone goes into teaching for the money", we are not thereby entitled to infer "those who teach do not need any money."

Therefore, 1., mustn't really be taken literally at all. And administrators who wave that piece of nonsense around as an explanation of why teachers shouldn't be paid more than they are deserve to be called liars, that is to say, people who tell falsehoods as though they were truths.