Your math is off. The home is an asset worth $150k plus a liability of $120k for the mortgage, for a net positive $30k. That puts your hypothetical person with

Your math is off. The home is an asset worth $150k plus a liability of $120k for the mortgage, for a net positive $30k. That puts your hypothetical person with a net worth of positive $130k, not negative $20k as you calculated.