The basis of this advice - in a nutshell is - put that extra mortgage payment into other investments that yield a higher interest rate than the interest rate on the mortgage.
A reasonable sounding bit of advice. With one flaw...investment markets are unstable, and unguaranteed.
The X% interest rate you're paying on your mortgage is a guaranteed X% investment return. Simply put, by saving X% interest on $100,000 through early payments - you've earned X% on $100,000 (amortized.)
By putting it into other investments, you're putting that value at risk.
If one prefers anecdotal advice - this is exactly what I did...put the money into a well-established, high-growth mutual fund with 20 years consistent returns.
In 2008.
2008!!!
Is this ringing any bells? Yes, I lost my shirt. Had that money been going against a mortgage, it would have continued making the X% gains.