You are completely correct, the people quibbling with you about statistics have not been paying attention to what is going on and are hopelessly naive about human nature and psychology. They are demonstrating exactly the bias thinking that caused the election results to be projected the way they were.
It wasn't just the New York Times, it was every single news outlet and every single poll. We have been running and studying elections for over 100 years, you would think, by now, that if we had any idea what we were doing, we would have long ago learned how to perform actual predictions using the data available to us.
When people break their legs, we can cure them 100% of the time because medicine has a strong answer for this problem based in thousands of years of medical science. Election polling and prediction is simply not in the category of "solved" problems.
If the statistics were really well understood...as some of the people arguing with you are claiming...WOULDN'T WE HAVE FIGURED THIS OUT BY NOW?
I have had these discussions about polls and statistics with my Liberal friends. Many of them are software engineers. Some of them even work in ML at large scale. They are utterly convinced that the data and statistics just need to be tweaked a little bit more and THEN they will be correct. To quote Donald Trump: WRONG!
There is a simple explanation for what happened that does not get into nit-picking statistical nuances. There is a simple explanation that does not allow people on the other side of the argument to bludgeon less educated opponents into silence by spewing technical jargon about polling data (which is really just a manipulation technique used to silence people by berating their intelligence).
The explanation is that the polling data was simply made up.
Or that many prediction models were created and only the ones favorable to the desired narrative were selected as being "Accurate" by people who are blinded by deep personal political bias.
This outcome scares people who prefer to see the world in a particular way.
People want to believe they aren't biased or that everything they read and see everyday is somehow "clean" or being presented by rational experts. That is a scary thought process...software engineers, in particular, cannot bear to believe that because it violates their underlying belief that the world operates in a logical way.
So instead of thinking like this, they crack open statistics textbooks and start reading chapter 4 at you. Its a defense mechanism to avoid reality.
There are direct financial rewards for telling people exactly what they want to hear. If Nate Silver and 538 consistently told people that Donald Trump would win, it is likely that their page-views would plummet into oblivion. Instead, the vast online hoards who like to be told whatever they want to hear and read news only to have their existing beliefs confirmed swarmed over Nate's websites, clicking on articles and gleefully watching the ads.
What is Nate Silver's punishment for being wrong over and over again? Nothing! There is no identifiable drop-off in his web traffic despite him and his team being wrong about everything this last election.
If what Nate Silver was doing was really "data journalism," shouldn't his following online have dropped off a cliff? It hasn't and it won't because what 538 is doing is not really backed by data and his readers and viewers are not discerning enough to care or believe that what they are reading is just opinion.
I am fairly disgusted by humanity at this point as a result.
Keep strong my brother, you are right. The people quibbling with you are living in an alternate reality where the media isn't incentivized by page views to gravitate towards narratives that result in more clicks. The media is dead.