I don't think it's sarcasm, just poorly explained. Owning a house serves two distinct purposes - as a home or as an investment. Despite what a lot of people think, it can't be both at once.
As an investment, you forego some upfront capital (downpayment), have some monthly costs (mortgage payment) and a monthly income (rent) and at the end you have an asset (current value) and maybe an obligation to pay another lump sum (principal - downpayment if interest only mortgage).
In the UK at least, for buy-to-let properties, the interest-only mortgage is common, so at the end of the mortgage term you have to repay the principal, and the profit comes from the different between the current value and the principal. In most situations, the rental income is almost entirely used to cover the mortgage payments, maintenance, costs, and paying tax, so during the mortgage period most landlords actually make very little income. It's essentially a bet on whether over the term (maybe 20 years), the difference in value will be better than the lost opportunity cost of not investing the downpayment elsewhere and the risk of periods of having to cover the mortgage and expenses without income during periods when the house is unoccupied, or tenants refuse to pay, etc. Particularly in the early years, the rental income may be substantially lower than the costs to the landlord, but over time, inflation will allow rental prices to increase but the mortgage costs will remain level. A smart landlord will invest the monthly profit at that point, to reduce the impact of the principal at the end of the mortgage.
In some ways, a house bought as a home is very similar, but in others very different. Typically bought as a home, a mortgage will be higher because the aim is usually to pay off all the principal as well as interest, and the simplistic view is that obviously having a mortgage for your home is better because you're always paying off the capital and end up with an asset at the end, the GP's point is that it isn't actually that simple.
Let's say you lived in the house. You're paying for the mortgage directly, let's assume that on average the mortgage costs are the same as the rent for an equivalent house, but actually at the start, the mortgage is probably going to be a significantly bigger chunk of your monthly expenses. On top of that, you have all the maintenance costs - some will be urgent and necessary, others can be deferred for later (although financially, perhaps not the best option because inflation will make the cost more or less the same now as later).
If you had the same house as a buy-to-rent property, you'd have the same maintenance costs and the same mortgage costs (whether it's interest only or capital repayment, the main difference is just when you pay it), so really the only difference is that you are receiving a rental income and losing the ability to live in the house.
As such, there is actually an equivalence between having a mortgage on a house that you live in and paying rent for that house instead - and the equivalent amount is the amount that you would have received as rent (minus taxes and costs from renting). If you could have rented that property out at £1000 per month, by choosing to live there, you are effectively paying that £1000 a month rent yourself.
In truth, the main factor in choosing whether to rent or get a mortgage is a mixture of availability and cost of credit (which varies depending on your financial situation) and how much you have available to spend on accommodation each month. Having a mortgage front-loads the payments - having a much higher payments initially, but fixed so that as inflation reduces the monthly cost in real terms, much cheaper later on, compared to renting where there is effectively a constant monthly cost in real terms once inflation is applied to it (probably annually, every time the price is renegotiated).
Personally, I'd chose a mortgage, because I was chose a cheap house compared to the area so that I was able to afford the monthly payment (the base mortgage was approximately 50% more than the equivalent rent would have been), and then used every bit of spare money I had each month to overpay, which meant that I paid off the house before the end of the mortgage term.
You might think that paying off the mortgage is an obvious success - I now own a house I can live in rent-free, but the alternative - paying much less each month and investing the rest, with compounding gains would probably be returning me an income that's equivalent to the rent that I would be continuing to pay if I didn't have a house.
Which one is better is down to personal preference, and also quite heavily influenced by societal norms - in the UK and USA, we're very strong believers in owning property, but in much of Europe, the vast majority of people rent and see no problem with that.