But the house usually does not go up 3% if you take inflation into account

Yes, but the purchase and loan are in nominal dollars. Taking GP's example numbers, a $500 house, bought with a $100 downpayment, in a house and general inflation environment of 3%pa, and an interest-only mortgage (to make the math napkin friendly)

  You start with $100.
  You buy a $500 house. $0 cash,  $500    in asset, -$400 in liability.
  A year passes.        $0 cash,  $515    in asset, -$400 in liability.
  A year passes.        $0 cash,  $530.45 in asset, -$400 in liability.
  After 30 years,       $0 cash, $1213.63 in asset, -$400 in liability.

That $100 turned in ~$814 of equity in 30 years. That equity has the purchasing power as today's $335. Even though inflation and asset prices rose by 3%, your $100 grew in purchasing power at a CAGR of 4.11%.

Contrast that with an unleveraged investment that also rose exactly with 3% inflation.

  You start with $100.
  You buy a $100 bond. $0 cash, $100    in bond.
  A year passes.       $0 cash, $103    in bond.
  A year passes.       $0 cash, $106.09 in bond.
  After 30 years,      $0 cash, $242.73 in bond.

Unsurprisingly, that $243 30 years from now has the same purchasing power as $100 today.

Your math ignored both maintenance and property tax on the home. Let's say maintenance costs 1% a year and property tax is 3.5% a year. I'm choosing both numbers lower than likely reality to give your position an advantage and let's say that advantage covers any income tax benefit of paying the property tax. After those 30 years you have a $1214 asset that you've put a bit over $1170 into - that's the original $100 plus about $238 in maintenance and about $833 in property taxes. So your $100 investment has grown by about $44 while the stock investment in your example, after deducting 20% in cap gains, has grown by about $114.

The house by itself is a bad investment, factoring in mortgage interest makes it even worse, then factoring in not paying rent makes it significantly better. How much worse or better it is in the final analysis depends on factors that are outside of many our controls - jobs, family, local market, etc. The decision is not quite as cut & dry as many on this thread make it out to be.