If you still owe money on your house. The argument is dont pay it off because you can write off the interest. Consider this:
If you make 100,000/year in salary at 25% thats 25,000 dollars. If you pay 10,000/year in interest on a mortgage and deduct it from your taxable income. Thats 90,000 on 22,500 in tax. It reduces your taxes by 2,500/year. Would you send a bank 10,000 to not send the government 2,500? If you didnt like having your house paid off, you could always get a loan.