Debt free vs Depreciating dollars when cash flowing

[Brian Naumann]

During my education process I've heard of two opposing points of view in regards to debt service when cash flowing rentals; 

Point One - Pay off debt as fast as possible. The theories I have heard are paying down debt with the profits to the point where your profits might reflect a $1 a month profit. Short term it seems like a grind and reduces capital that could be used for additional investments or owner's profits.

Point Two - Pay normal payments over the life of the mortgage. The theories I hear regarding this one is that over time the dollar (or whichever currency you use) is worth less and less. So in theory what might seem like a huge payment in today's dollars might be equivalent to pocket change or a cup of coffee in a decade or two due to inflation. (Think about Robert Kiyosaki paying a dime for comic books in the 50s that today run about $6-7)

I'm curious to people's opinion on this. 

Please, if you respond to this post respect everyone's opinions that also responds on this topic. I don't think there is a "right" answer so nobody can be wrong.