They missed another point - what if you loose your job?
THAT is one big point that always seems to be missed. IMO- mortgages are not beneficial to the person who has to pay, it is only beneficial to the lender. People tell me about the "tax write-off" or some other silly benefit they get from having a mortgage, and I laugh. What they mean to say is: I never did the math required to determine how much I would have to pay over the life of the mortgage that has a minimum down payment.
It's always better to pay it off as soon as possile.
Actually its not always better.
Suppose I got a $100 raise. Among the options I considered was putting the $75 I received after taxes into a house payment or putting the $100 pretax into a 401k in a bond fund paying an interest rate identical to my mortgage or putting the $75 after tax into a Roth 401k. You have to make assumptions about future taxes, but in most situations, the value to your portfolio is about the same. You will still owe on your house a few more years but you have the cash on hand to pay it off early.
The advantage to investing is liquidity. The Roth and the 401k can be pulled out and used for any purpose. To realize the equity in your house, you have to sell it or borrow against it. Added to that is the fact that I keep my small tax deduction for a few more years, so in the end, a safe investment in a tax-smart fund versus putting it into equity really gives a financial advantage toward investing as long as the loan is in place, certainly while the interest payments are deductable.
So given the chance to invest in paying off a 5% mortgage with after tax dollars or investing at 5% with pre-tax dollars (while deducting the mortgage interest), the answer isn't always obvious. In my case, investing works somewhat better, and I can pay the house off today if I need to. Plus I can create cash to use for something else if I need to without going into debt.
Not saying your approach is wrong, because it probably isn't for you. But this approach is better for me. When you have cash on hand to cover it, debt isn't always bad.
At
http://www.vertex42.com/Calculators/loan-calculators.html
there is a free excel template that can answer the question of tax implications, interest amortization and the benefits of prepaying a mortgage.
This is not intended as spam but was a great tool in my wife and I deciding how to allocated unexpected income.