Of course a house with a mortgage counts as net worth. Let's say you had paid off $999,999.99 of a $1,000,000.00 house, meaning you owe 1 penny to the bank. You have a claim on the $999,999.99.
On paper, it's a horrible asset class compared to stocks. In fact, viewed from a historical perspective, a house has a negative real yield because taxes plus maintenance are higher than appreciation.
Stocks vs. House:
* Historical annual appreciation: ~10% vs. ~2.2%
* Past 10 yrs annual appreciation: 9.3% vs. 6.5%
* Annual carrying cost: 0% vs. ~4%
* Liquidity: High vs. low
Most people who say that they "profited" $1M because they bought a house for $500k and sold for $1.5M a decade later (something which is an anonolous increase you find in only a select few locales in the U.S.) conveniently forget that over that period they paid $100k in property taxes, $60k to replace the roof, $100k for the bedroom addition, $150k in HOA fees, $50k in attorney fees when they got sued by a pedestrian who slipped on the sidewalk in front of their house, etc.
But owning a house is a good idea from a lifestyle perspective. Renting may be better in monetary terms, but by the same token you could say that living in a van is better than renting a house. If you have kids, you don't want to potentially have to move to a different neighborhood every year. Most importantly, there's only a finite amount of space for building single-family homes in a zip code, and in popular areas that space is already used up. Let's say there's a house on a 1-acre lot, built 50 years ago. There will never be a new 1-acre lot allocated for a new house, because it's more profitable nowadays to squeeze 12 townhomes onto 1 acre. Thus the price of the house on the 1-acre lot is only going to increase, fast. If you want a house with an acre lot so your kids can have pool parties and a sport court and you can have a garden and rockery and one of those half-circle driveways that goes up to your front door, best to purchase one sooner than later. Same idea living in a nice neighborhood. That fact is that non-nice neighborhoods never become nice ("gentrified" doesn't equal nice) and nice neighborhoods don't usually become non-nice (extreme example would be like Detroit or Buffalo, where once-ritzy neighborhoods are abandoned). So locking into a house in a nice neighborhood can be a good life investment.