EDIT: Ah I see they were implying they went from $200k net worth to NEGATIVE. I hope the transaction costs were less than that!
To them any debt is bad no matter what it is and drags down their calculation of becoming a millionaire. Their calculation for net worth is all savings minus any form of debt.
A mortgage is different, by getting a mortgage and buying a house, you build up your assets with every payments you make, it's often better than paying a rent and not getting anything in the end... The main difference between a car and a house is that the house generally doesn't depreciate, which is why a mortgage can be a good investment.
There are a lot of variables in play, but buying a house with a mortgage can end up being better financially than renting. There are a lot of factors to consider. If renting is worse than home ownership, and you hold off buying until you can do it without a mortgage, you may lose out. Additionally, if you can get a really low fixed-rate long-term mortgage, but you invest in long-term total market index funds, historically, you'll come out on top over having paid cash for the house.
Also, if debt is bad (and I agree), do these people live with their parents? Because that's the soundest financial move possible.
Here's an example:
Let's say today you have $100,000 cash in your bank account and no other assets to your name.
Your net worth is $100,000.
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Now let's say that you buy a house tomorrow for $500,000. You put 20% down ($100,000) and secure a loan from the bank for the final $400,000. Here's your new net worth:
Asset: House $500,000
Debt: Loan ($400,000)
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Total: $100,000