It can. The housing market doesn't impact all properties across the board, and some neighborhoods get away unscathed while others are devastated.

In the worst case scenario, having a downturn can cause a "buyer's market", where there are more people trying to sell their house than there are prospective buyers, so they have the power to negotiate much better deals. If you purchased your house 10 years ago for 200k, and in that time it appreciated to 400k, and then there was a sudden market downturn and it lost 50% of it's value, your house would be worth about what you paid for it, but all your equity is gone, so you don't profit but you are also not totally screwed.

If you bought your house for 400k right before the market downturn, you will be "underwater", and own a property that is worth less than what you paid for it, meaning that if you tried to sell you wouldn't get enough to cover the mortgage you owe to the lender. Forget about profit at that point.

If you plan to live in the house you are in now until you die, then none of that matters at all, really. In fact, having market downturns benefits you in that scenario because if your property is worth less money (relative to all the properties around you) you pay less in taxes and insurance. But most people don't plan on living in the same house forever. They might want to move to a nicer house, or one in a better location, or downsize when their kids move out, etc. so it's usually seen as a bad thing when the market crashes because you have to spend years building equity and loan amortization means that for the initial few years of your mortgage payment, you are basically paying off the interest only and barely denting the principal.