If banana was arguing that training teachers will cost nothing, then that is indeed absurd. However, as I recall, he was talking about guards (even you said officers, not teachers), who already undergo training, therefore the additional cost of training guards should be zero because they should already be being trained to a high standard. What extra cost is there? The extra cost is the salary of the guard.

Teachers, well if we're training them, then sure that costs more money, but it might be less than an "officer" whose sole duty is to guard the school, as opposed a teacher who has duties beyond being a guard, such as teaching. Perhaps there will be greater value.

One way or another, I don't see that cost is really a relevant issue. The morality and sanity of arming teachers is open to debate, but surely you take the extra cost on the chin? It'll be peanuts compared to what governments collect in tax revenue.