That's my point. What if interest rates are 10% or 15% when I need the money in 10 or 15 years? What if I have no job or lower income at that time and a bank won't lend me the money because I can't pay it back?
Let's say you have a house worth $250,000 and it is totally paid off. You lose your job. You now need $50K or $100K of that money. You can't get it - you won't qualify for the loan. But you say "it's my money"! No, it's not. It's your non-liquid asset.
If I would have been stashing some of that money away as cash instead of putting it all the house, I'd have some of that money to live on.
BTW, I'm not totally discounting the idea of eliminating debt. I'm debt free except for my mortgage. But mortgage rates are at historic 40+ year lows. Why not take advantage of it?