I see what you are saying, you are a perfectly good teacher. I disagree however with your figures; in my case, comparing two actual loan offers, I am paying more interest from month one with the 30 year, paying the same amount as the 15 year - it doesn't matter how much principal you pay, the interest is greater because the rate is higher, right? Anyway the figures in front of me say take the 15.
Secondly, and see my last post to train, my goal is to build equity as fast as possible. I own about from 25-40% of my home (depending on who you ask), and I want to own it all in the event of economic calamity. If I had the means to pay the balance tomorrow, then I would absolutely agree that what you are suggesting is a good idea, not great, though, as you are effectively using your home equity as margin. No thanks.
For my goals, the 15 is the way to go.
thanks for the advice.