It's pricing the cost of shelter. Renting a home is buying shelther. Buying a home is buying shelter and buying a financial asset. OER is the way you separate the last two components. Otherwise, you'd have to only look at rents to determine housing prices, which would be rubbish in a country where most households live in homes they own.
Which flows through to owner-equivalent rent, in part.
> In CPI thinking these are equivalent forms of shelter, but I bet if you asked most Americans, they would not agree with you
It really doesn't. When measuring rent, you directly measure rent. For OER, you're measuring the housing price and imputing shelter cost from that. They're similar, but different. Sort of like how renting and owning are similar, but different.
Also, given the variance in housing affordability across the country, you'd almost certainly have to strip out any financial-asset component anyway to meaningfully compare the resulting number.
American education.