I'm not arguing that they're obviously not making a profit, but saying that it has to make a profit is not necessarily true. I mean, overall they must, but they don't have to make a profit on each individual service that they offer.

Sometimes there are non-obvious ways that banks can make profits. For example, a bank can offer a free checking account by paying for the costs with interest on the balance. The mechanism for that is easy to understand, but your average layman would not think of it on their own. So I don't think it's unreasonable for a layman to trust a bank when they say "no fees", and assume that the bank has some clever way of profiting off of the transaction without hurting them. It's a wrong assumption, but it's not unreasonable.

In this day and age, we should be forcing banks not to flat out lie to customers. Spreads are another thing they seem to be able to shamelessly lie about without any apparent fear of punishment.