Why does F. Scott Fitzgerald divide characters into "old money" and "new money"?

In The Great Gatsby, characters that come from old money are almost invincible. Not only do they have material wealth to buy the things that they want, but they exist within a social status that will keep them protected. This old money attitude is most apparent in Tom, Daisy, and Jordan. Old money carries the feeling of always having been a part of the upper echelon of society and of always remaining there. There is a confidence and freedom to old money.
New money is embodied by Jay Gatsby. Although he can throw grand parties that many will attend, he can be easily tossed aside. No amount of money alone can locate him within the elite old money circle. No one even attends his funeral.
F. Scott Fitzgerald makes this distinction in order to illustrate that money and social status are not totally the same thing. Daisy and Tom have the privilege to move through the narrative unscathed, because of their old money background. They have the confidence not to care what others think of them. They can just move on.
Gatsby on the other hand does everything in his power, for the full extent of the narrative, to try and win the affection of Daisy, and the acceptance of those with old money. In the end, he doesn't receive any of it.