What do people mean when they say "this is why we can't have nice things"?

“This is why we can’t have nice things” is an idiom. It connotes a more complex layer of meaning since its origin. Here’s a good definition: A phrase used to blame someone or some group for engaging in the kind of behavior that has led to something valued becoming damaged, ruined, or corrupted.

In a 21st century context, it means this:

… it voices the earnest class aspiration of a dupe who believes that "things" are "nice" (a humorously innocuous word) based on some standard class grid. Then anything that goes wrong points to the larger (comic) frustration of not being able to achieve the standard class-inflected goal. Like Ralph Kramden or Lucy in I Love Lucy. 

The decontextualization of the phrase makes the writer or speaker (not the character) and the audience in cahoots against the position of class dupe.

What's it like to be a member of an Ivy League university's secret society?

If sworn to secrecy, such individuals are unlikely to answer, even as Anon on Quora.

We know that some of these societies exist e.g. Skull & Bones. My father was at Yale in the 1940s and told me that it existed, not that he knew more about it than someone who never went to school there. 

I went to Wharton, 50 years later. University of Pennsylvania is an Ivy League school but generally considered a lesser one. There was a rumor, never anything documented that I ever read, of a secret society for the 2nd year MBA's. 

It worked in the usual way: A fixed number of students, maybe 15 or 16, were asked to join each year. They were the "power elite" of Wharton Business School, and passed their spot on to successors upon graduation, but remained affiliated throughout their working lives. Only men were members, in keeping with tradition. I forgot the name of it, don't know if it even existed, or was just something UPenn students made up, so they would have a secret society of their own, like the other Ivy League schools!

Who is Sidney Blumenthal and why was Hillary Clinton contacting him via private email?

Sidney Blumenthal is the father of Max Blumenthal. Max is not a fan of Israel. It is peculiar how Sidney is such a neoliberal Hillary fan yet so defensive of Max. Clinton Adviser Sid Blumenthal's New Cause: His Son's Anti-Israel Book (2013):

A veteran confidant of Hillary Clinton has waded into a bitter argument over the explosive topic of Israel, defending his son’s intensely anti-Israel book from a liberal critic. 

Sidney Blumenthal, a former New Yorker writer turned Clinton adviser from the White House to the 2008 campaign, has been waging an online campaign against Nation columnist Eric Alterman for negatively reviewing his son Max Blumenthal’s book, Goliath. The book was described by Alterman, himself a frequent critic of Israel, as “awful” and something that “could have been published by the Hamas Book-of-the-Month Club (if it existed).”

Clinton Foundation officials refused to respond to questions of whether the elder Blumenthal is currently on a Clinton payroll.

Sidney contacted Hillary by private e-mail during the her destabilization of Libya because he had various business ideas, for himself, and wanted her feedback and insights. He stopped after the U.S. ambassador was killed at the consulate in Benghazi. Hillary thought Sidney was very insightful, and had been forwarding excerpts from his emails to her staff and friends for years. 

Sidney Blumenthal's Mosaic Mugshot by Kevin Vaughn, on Flickr

Sidney Blumenthal, a senior Hillary Clinton campaign adviser and former White House aide to Bill Clinton, was arrested in January 2008 for drunk driving in New Hampshire, one day before the state's presidential primary. 

Blumenthal, 59, was popped by Nashua cops after his rented Buick was pulled over for speeding. When Blumenthal, pictured in the below Nashua Police Department mug shot, showed signs of intoxication, a cop gave him a field sobriety test, which the Clinton operative failed. Blumenthal, who declined to take a Breathalyzer test, was booked into the Nashua lockup on an aggravated DWI charge.