It’s a liability in two ways:

First, even if you owe nothing on it, the investment is illiquid. To get access to its value for an urgent reason, you have to borrow against it, putting yourself in debt. If you sell it, the only way you can realize a true profit is to buy another dwelling that costs a lot less, which you may not want to do.

Second, anything you owe on it is debt. Debt is debt is debt, no matter what anyone says about “good debt” and “bad debt.” On the surface it’s less malignant than credit card debt. But it still goes on the liability side of your ledger.

My contrarian point of view is that paying off your house gives you a lot more income to put into liquid savings that you can spend in emergencies or live on in retirement. And it allows you to live on a modest salary without having to pinch every penny that passes through your fingers.