Why the pitch sounds right
Every sentence in it is true. Cash on the mortgage does save interest. A new car does come with a warranty. Repair bills on an older car are real. The conclusion is still usually wrong, because of what the pitch counts and what it leaves out.
What it leaves out
It counts repair bills, because they're frightening and arrive without warning. It doesn't count depreciation, because depreciation never sends an invoice. A new car commonly loses more value in its first couple of years than an older car costs in repairs over five. No warranty covers that.
It also turns the monthly car repayment into background noise. That repayment is the biggest number in the whole deal. The green box shows what it would do on the mortgage instead.
When swapping can make sense
If the car you own is genuinely unreliable, unsafe, or about to need an engine or gearbox, put those costs in the repairs box and run it again. If your job depends on a car that starts every morning, that's a real cost too. The point isn't that nobody should ever buy a car. It's to see all the costs before you decide.