With interest-only mortgages the payment will go down each month as it is amortized gradually. For example, if with 30-year loan has $1500 a month and you only pay $1200, it equals with $300 cash flow difference. In current economic situation, money is king! If you can reduce your payment $300, it would mean really a lot as it means you 'earn' $3600 annually. Everyone surely loves such a huge amount of cash as it can be used to pay the principal which may make the mortgage payment faster.
You can also use the extra cash in a safe vehicle where you can earn interest from saving account. In ten years, you can have nearly $40,000 which is a significant amount of money and would be useful as an emergency cash fund. The cash wouldn't be locked in your property and it is safe, accessible and makes free money for each month. With interest-only mortgage you can earn money while paying off your house.