Note that Warren isn't claiming that everyone is poorer, rather specifically middle-class households that chose to buy expensive housing to get into better school districts. Her argument can be read as saying that housing/education inflation is higher for those families specifically (and therefore lower for everyone else - if it's higher than average for some it must be lower for others, that's the nature of averages).

Also this is unrelated to my point, which is that OP has a misleading and borderline false title.