This is mixing up liquidity with asset vs liability. A house is a depreciable asset. The land beneath the house holds it's value and doesn't depreciate. That's why the assesed value for tax splits them out. Both are less liquid than cash, but I can convert my equity in the asset to cash very quickly with a loan, or put the house up for sale and maybe it takes a little longer to get the cash. The loan would be a liability. But a house is never a liability on financial terms.

My current plan is to buy, live in the house for a few years, offer the house up for rent, and rent a new house for myself. I'm currently on step 2. I don't want to overcommit myself in real estate so buying a second residential property doesn't make sense for me. Because of rent appreciation I will have positive cash flow while renting out my current home. That hedges for any future rent increases in my future place of residence.

I'd consider buying an income generating vacation home too. But not another primary residence. That's just my opinion. And my opinion doesn't make my house an asset or a liability.

Now that said, I feel one non-financial aspect where owning a house is a liability is the opportunity cost of time spent maintaining the house. In a rental the landlord takes care of it.