Let me try a simple but mathematically real example to see if it helps explain my distaste for Dave Ramsey's methodology:
Couple A & Couple B both take out $375,000 mortgages at 4.5% to buy a home worth $450,000 in 2014.
Couple A pays an extra $1,000 per month towards principal, thereby paying off the mortgage in almost exactly 15 years (14 years, 10 months to be precise). At that point, they have a home worth $600,000, no mortgage debt, so effective equity of $600,000.
Couple B pays the mortgage as scheduled and invests $1,000 every month in a brokerage account earning 10% per year. In 15 years, the brokerage account will be worth $401,000 and their home will be worth $600,000. They will have a balance remaining on their mortgage of approximately $249,000, giving them effective equity of $752,000.
Couple B is $152,000 ahead of Couple A in fifteen years and has $152,000 to keep working in the market, versus Couple A which is just getting started. Just as importantly, should Couple B decide at that time to pay off the balance on their mortgage, they are still $152,000 ahead of Couple A after paying off their mortgage in full.
I realize the world's not perfect, markets (both equity and real estate) fluctuate, but borrowing money cheaply and investing it wisely is mathematically always going to win in the long run.