They also neglect the Mortage Interest Tax Deduction and State and Local Tax Deductions, whcih reduce the cost of both by your marginal tax rate, and is a big benefit towards owning.
More importantly, this neglects that buying a home is locking in the price for the long term for the majority of your housing cost. Buying usually is similar all in the first year, but after 5 years your mortage payment is the same while rent has probably gone up significantly.
Not everyone benefits since many people take the standard deduction.