The apostrophe actually makes it a contraction, not possessive. So they're really saying "the underpaid teacher who bought it with it is own money". I know not everyone cares, but that's how our weird language works...
Who's obsessed? It's a joke about a dude attempting to man-splain even when they're wrong (I'm a dude and I've definitely seen it) and her turning the tables on him. That's it. To get defensive about that is... weird.