Why does author ignore home equity in scenario 3 (when house prices track with inflation). Paying $1.75M to own a house is more savvy than paying $1.3M to rent

Why does author ignore home equity in scenario 3 (when house prices track with inflation). Paying $1.75M to own a house is more savvy than paying $1.3M to rent over 18 years as you can still sell the house for $1M. I didn't buy a home as an investment with the hope that the value will appreciate: I bought it so that I can build equity instead of paying rent every month and getting nothing. The only way home owners truly lose money over renting is when their total expenses[1] after selling the house is greater than the rent they would have paid for the same home over the same period. My home could lose value by a significant amount over the course of my mortgage, and I'd still come out ahead of renters because of equity. 1. Maintenance can get expensive