<< So, if anyone can explain this, why not pay off as much debt as possible before lowering taxes? On the other hand, why should we pay off the debt? If you can try to phrase these in terms I can understand that would be appreciated. >>
The idea behind "good debt" is that by incurring costs now, it will lead to a higher payoff in adjusted terms later on, or that the need is great enough to justify the deficit spending in the here and now. Let me give you a couple of examples to demonstrate the principle to you.
Example 1: You're 22 years old, and have a choice to make. You've finished your undergraduate program, and are working a so-so job which pays the bills, but you want to go to medical school to become a doctor, but can't afford tuition. As a doctor, you'd make a significantly higher salary than you do now, but you have to go to school first before you can become a doctor. You are trying to decide whether to stay in your current job and pay off your current college loans, or take the plunge into medical school (knowing that you'll have to borrow more money to do so).
This would be an example of deficit spending, with the intent being to spend a bit more now, to earn a lot more later.
Example 2: You're 23, and medical school didn't work out. You have no job, and no cash in the bank as you spent what you had on medical school tuition. You have no food in the 'fridge, but you do have a credit card. You are trying to decide whether to borrow money by buying groceries with your credit card (deficit spending) or starve to death.
This would be an example of emergency/contigiency deficit spending.