Equity isn't relevant to the argument, that's why.

The argument is simply that by living in a house yourself, you are effectively paying rent on that property at the same rate that the house could be rented out if you were not living on it.

Any equity gain in the property itself isn't relevant to the rental value discussion, rather the separate transaction between you and the bank, whereby they lend you money up front to buy an asset and the terms by which you repay that money and the capital gains on that asset in the mean time.

The potential rental income of a property may be similar to the value of the mortgage payments, but generally won't be over the lifetime of the mortgage. As I stated 2 posts up, the cost of a mortgage is front loaded, so the price you pay on a mortgage at the start is generally more than the equivalent rental price would be for the same house, and towards the latter stages of the mortgage it will be much lower, because the monthly mortgage payments are still the same but the real-world cost of those payments has decreased due to inflation.

The simple point is that any time you choose to live in a property, you are either paying rent for the privilege of doing so, or you are missing out on the rental income from someone else who could be paying you to live there instead.