If you go with the concept that your house is an investment, you’ll see that it doesn’t make a lot of sense to sink everything into a single investment. You could just as easily get a loan to buy $200k worth of gold. The weird thing about a house is that you get to do something with it. Alternatively, you could also buy a rental property, that pays you more than the amount of the loan.
Like your father said, paying off your mortgage means all of your money is tied up in the house. This [may] put you in a position where you need to use credit card debt to pay for near term expenses (like auto repairs), or need to take out a auto-loan where you otherwise wouldn’t need to.
From my personal standpoint, when my wife and I bought our house, we used some of our medium term savings to put down 20%, that meant we didn’t have to pay for mortgage insurance*–that makes a significant difference to our monthly payments. Any more than 20% and we didn’t see much of a change in our monthly payments for a 30 year mortgage.
It also meant that the house we could afford was based on how much we wanted to use for that 20%, which was lower than 3 times our income.
From there, we also shifted some of our medium term savings to become part of the house payments. Instead of investing $X a month in the stocks or bonds, we invested that $X in a house.
But in this situation, the cost of our mortgage (plus taxes and insurance) was considerably lower than our rent–and we are investing in real-estate.
*This is an example of how by renting cheap and saving, we were able to avoid a situation where we lose money to mortgage insurance. We could have used that money for a better apartment. But mortgage insurance is a cost that doesn’t get us anything, and is effectively a tax on the poor or the greedy.