Because to invest before your house is paid for (outside of a 401k or retirement plan) is basically borrowing from your house to buy securities, stocks, bonds and mutual funds.
You are borrowing at 4-5% to hopefully get a return higher than 5% and pocket the difference. The key word is hopefully. A lot of things have to line up for that to work.
Guess who is propagating this theory? Thats right, the brokerage industry. They want nothing to do with you paying off a mortgage. They need assets so they can collect commissions, concessions and fees!
I know its not very sexy to pay off your house and its cool to talk about your stockbroker or investment portfolio at parties but if you think logically for second, when you pay off your house, you are guaranteeing yourself 4-5% (or whatever your current mortgage rate is) and you just may enjoy a slightly less stressful life knowing your house is paid for.
Additionally, some states offer bankruptcy and lawsuit protection for your primary residence so thats nice too, just in case.
Yes, I know you'd be missing out on the mortgage deduction come tax time but it has always seemed rather pitiful anyway but I am no tax guy.