I also didn't understand the marginal aspect of tax brackets myself until about the same point as OP. We only ever talk about tax brackets as a percentage, I feel, so that aspect just never comes up. It's an easy assumption to make.
(And even if you feel like that assumption is nonsense, since it results in absurd situations like an income increase resulting in a net loss: I would say most Americans don't expect the laws or tax code their government makes to behave sensibly, so this just isn't a red flag.)
> How can we have a serious conversation on tax reform when people don't know what system we have now?
We have this issue in a number of areas, not just taxes; e.g., tech issues (encryption, net neutrality) in politics.
(And I find this happens a lot, not just in politics. For example, I feel that I've run across a number of people who think that because C++ lacks garbage collection, that C++ code must therefore be littered with manually new/delete calls; thus, GC is "better", because folks don't realize that an alternative, RAII, exists.)