Okay I looked at some numbers. If interest rates are low then carrying a mortgage makes sense. You can either choose to stack cash inside your house or outside. Obviously having it outside your home gives you more flexibility on what to do with it. Hopefully you can invest it somewhere at a rate of return higher than your mortgage for a little arbitrage like he is mentioning in reason #10. But it doesn't work if rates go up from today's very low rates. Reasons #2, #3, #6, #7 all assume low interest rates, inflation, and never ending exponential growth in the economy. Rising interest rates are generally deflationary. But since we live in the present and the future is unknowable, lets work with that.
His math given in reason #10 is a slightly rosier picture on Smart Sam's net worth than it actually is, as Dillon noted. He shows that that Smart Sam's investment account is $94k ahead of Nervous Nick's. But that isn't the same as net worth. Nervous Nick's remaining mortgage balance is 150k and Smart Sams is 217k. Nervous Nicks net worth 150k if he sells the house. Smart Sam's is 177k if he sells his house, which he might have to to find a new job anyway. Smart Sam is ahead 27k, although he doesn't have to sell his home right away like Nervous Nick. If they lost their jobs because the economy is tanking and along with it home prices, Smart Sam may be upside down in his mortgage.
I do see the appeal of having cash stacked outside the home and the math works at today's interest rates. Lets assume two scenarios A and B for purchasing a $200k house with 20% down.
Sam the 3rd
30 year mortgage @ 3.5%
Angie the 2nd
15 year mortgage @ 3.0%
Sam invests the extra $387 he didn't spend on mortgage @ 5% for 15 years. Investment account $101k
At 15 years Angie now invests her payment @ 5% for 15 years. Sam continues to invest $387. Sam's investment account is $310k after 30 years, Angie's investment account is $288k. Sam has $22k extra at the end of 30 years, equivalent of making an extra $733 a year. Obviously the gap between the two would rise with a higher return on interest. If you raise the return to 7% the difference is $105k or at extra $3500 a year.