How can I argue that Pride and Prejudice is an analysis and criticism of traditional class and social distinctions? What mode of organizing society...

Pride and Prejudice helps us to see that a society based on structures that privilege money over integrity and status over intelligence is a faulty one.  Just because a woman is a lady of great fortune does not mean that she deserves to be lauded and sought after as though she is a great prize.  On the other hand, a woman of lesser means who possesses superior intelligence and wit should, perhaps, be considered more of a catch rather than a temptation to be avoided.  Privileging certain members of society based on arbitrary distinctions such as status -- something conferred upon those who happen to be born into the right families -- instead of privileging those who exercise good judgment, be they high or low, unjustly creates misfortune for those deserving of respect and admiration. 

For example, Lady Catherine de Bourgh takes serious issue with Elizabeth's classification of herself as on a level with Mr. Darcy, though Elizabeth -- due to the force of her intelligence, wit, and sound judgment -- is certainly more deserving of respect than someone like Caroline Bingley or Mrs. Hurst.  In a more just society, Elizabeth would be considered far superior to either of them.  Austen seems to offer the qualities that Elizabeth (or Jane) possesses as a better way of determining which members of society should have the most value.  Someone like Miss Bingley ought to be classed lower than Elizabeth because she lacks good judgment and good manners, integrity and wit.  And despite Elizabeth's relative poverty (and unfortunate relations), in a just society, she would be raised up.