I feel like this is the biggest point of contention with the series, at least in the west, and for the most part the ones who get it are those who have have gone through mental issues of their own. People that haven't, and even a fair amount of people that have, don't see that and just see detestable characters. Despite that, it's still universally regarded as amazing and influential.
That is exactly why I liked the characters and the ending of the show so much. not going to drag us down to RealGAF again but it hit close to home.
Yeah, I don't like getting into Eva arguments, but this is how I feel aswell.
Eva is my favorite anime, and the only other one that has come close is FMA.
The characters in Eva shocked me by how developed and 'real' they are, there weren't any dumb macho heroes who win everything because they're so cool, they're kids dealing with horrible situations and lives and they grow accordingly.
People like to make jokes about how weak Shinji is, but the reality is that he is one of the strongest characters in anime, because he actually had to face real depression(not angst) and he overcame it despite his life getting worse and worse through the series, and he came back from snapping beyond rock bottom.
I rewatched it recently thinking "man, I might be giving it too much credit", but then the characters were even deeper than I thought prior.
I will easily say that Shinji is my favorite character in anime, and possibly media in general. Hit close to home, and it hit perfectly.