What people need to remember about Evangelion is that series creator Hideki Ano was mentally ill at the time he produced the original series.
Ano was, at one point, a respected director and creator; among other things, he was behind such famous titles as Nadia: Secret of Blue Water (which people have alleged Disney ripped off to create "Atlantis").
However, he wound up doing a stint in a mental hospital for depression and exhaustion; one account I've seen has it that he checked himself in. Ano was eventually released, at which point he began work on what would become Evangelion. Ano's goal was to "deconstruct" the whole "giant robot" genre by taking all of the various cliches that are usually at work and playing them lethally straight. His idea was to show what it would "really be like" to be a person in that particular character role and situation, but for reasons unknown he failed to make his point clear. Instead, people took Evangelion at face value.
Adding insult to injury, a large portion of the Evangelion fandom actively rejected the official pairing of Shinji / Asuka. Many fans paired Shinji off with Rei, while many others paired him off with Misato.
Ano's frustration with the series not being taken seriously combined with his distress over the rejection of the Shinji / Asuka pairing caused him to have a mental breakdown halfway through the series. As such, about episode 13 or so things start getting dark, moody, and depressing. It's been hypothesized that this was in an effort to hammer the point home while making the alternate romantic pairings as unpalatable as possible, but at this point it's anyone's guess, really.
And as if that wasn't bad enough, Gainax was in deep financial trouble at the time. Gainax was under contract to produce 26 episodes, but they only had enough material for 24. The original plan called for the show's final battle to take place across the last two episodes in order to meet the contract, but by the time episode 24 was done the budget was gone. To compensate, Ano infamously decided to have the final two episodes reflect the mental battle inside Shinji's head as he was fighting, and then hope that he could scrounge up enough money to produce a movie as a proper final chapter.
The fandom flipped out.
People were quite upset as it was with the second half of the series. The final two episodes pushed folks so far over the edge that Ano actually began receiving death threats. Given Ano's already-precarious mental state, he, shall we say, handled matters quite poorly. The end result was End of Evangelion, which went completely over-the-top when it came to destroying everything; the final two episodes of the series did hint at things being bad (you actually see the dead bodies of two of the main characters), but it's now believed that End of Evangelion was more about Ano sticking it to his critics than anything else.
Suffice to say that the staff at Gainax immediately staged a mutiny once everything was said and done. The staff shoved Ano aside and went right to work on FLCL, with Ano's only input being to voice the family's pet cat. The one-two punch of Eva and FLCL wound up giving Gainax a reputation that it still has not escaped from, even with such titles as "His & Hers Circumstances" under their belts.
The "Rebuild" movies were originally sold as being what the show would have been like had Ano been in his right mind, but the addition of Mari pretty well blew that out of the water.