Financially, if you have a mortgage in the ~4% or lower range, with an effective after-tax interest rate of <3%, it probably makes little sense for most people to pay any more than the standard monthly payment. That said, I can see two justifications that make sense.
First, as you see some people here saying, there's the "freedom" and "convenience" factors to no longer having an outstanding mortgage, i.e. feeling free because you are no longer indebted, and no longer having to make sure you have money in a certain account at the right time every month to make the payment, etc. Thus, you may fully acknowledge that on a pure financial basis, you'd be better off paying only the minimum and investing the rest, but you are willing to suffer some inefficiency in order to feel free and have greater convenience, just as you pay extra for many other luxuries in life.
Second, it may make financial sense or at least be a wash for some sets of individuals. For those with little income, low tax rates, and a small mortgage, the interest deduction may not be very valuable, so their effective interest rate may be closer to the 4%. Moreover, having a mortgage is the same as being short a bond. For those who are already retired and/or are older, a reasonable portfolio is some mix of stocks and fixed income. Paying off a mortgage in lieu of buying treasuries and being long treasuries / short mortgage makes for a simpler portfolio that does basically the same thing.
Personally, I am in my early 20s, just entering the workforce, and will have (a) a relatively high income, (b) face high tax rates, and (c) am at a stage in my life where I want to have almost all of my assets in equities. So for me in a few years, if I buy a house, paying extra towards the mortgage would be a terrible idea, but it depends on your situation.