I have been witness to a couple dozen animes, and actually watched a few hundred episodes of some of them. I've also read some manga. Several of my friends growing up watched a lot of anime, and I just wanted to say why I don't like a lot of it:
0) I am mostly focused on characters I like, and theme, in my fiction. I can watch Smallville because I love Superman, but if Superman was not the main character in that show I wouldn't watch it if you paid me. If a show or book doesn't have a character I especially like (who's usually the Elric/Conan/Cugel type, a ubermensch with philosophical tendencies). A lot of my problems with anime boil down to what I assume are elements of Japanese culture and the authors' taste that just don't appeal to me.
1) The Art. I like 'romantic realism', i.e. people that look like real people, if real people looked like superheroes. Alex Ross, Frazetta, and Osprey military manual illustrations are my bag. Anime's anatomical wrongness bothers me even more than Rob Liefeld, and I can't really like a character who looks goofy to me.
2) A lot of the adult characters are extremely immature, afraid of women, hyper-emotional, etc. I do not like this in real people, much less my protagonist. This is related to:
3) I don't like children protagonists. I don't really like children (I didn't when I was a child), because I'm very serious and anti-drama. Children are like walking bastions of noise and trouble.
4) Probably my most autistic reason, I find a lot of the sexual stuff boring and relationship drama irrelevant. I am hardly a prude, but I'm more just asexual. I think it's a very simple, fairly easily understood, psychological disability that afflicts normie breeders. I find the constant sexualization of characters, and the attendent relationship drama, to be uninteresting. I can't really be bothered to talk to women unless it's about nerd shit, anyway, and so I just don't care about a whole part of the human experience that other people (especially children) seem to find fascinating. If I am seeing a relationship in fiction I prefer it to be two monogomous adults responsibly raising their children. People who are always at odds should just stop dating, and the insistence of staying with people you can't get along with is no more respectable than a drug addiction. It's bad for you, expensive, and nobody else wants to see it. Also, the world is about to end and you're obsessing over getting laid? Prioritise shit better.
5) A lot of animes are too damn long without much to justify it. Filler out the ass, like bad fantasy novels. I have very little patience for watching shows, because books are almost always a better use of my time, and if you're wasting hours of my time on charging up and long close ups of people making faces, I'm already done with your show.
6) Anime and its version of fantasy are vigorously at odds with the oldschool dark fantasy, Tolkien and D&D save-or-die fantasy. Main Character Syndrome is turned up to 11 (50% of all anime characters are more OP and snowflake than Elric of Melnibone), everyone has to be something fucking weird, and obsession with character drama and backstory overrides the actual fucking plot. Elric is already the borderline of how much drama and convenient super powers I can put up with in fantasy, and anime characters are often way, way over that line. The Japanese have taken what they want from European culture and put their own spin on it, and, frankly, I prefer the original. This has infested a lot of modern RPGs, where people have conniption fits because you tell them their loli just got killed by a kobold in the first fight.
Even the shows like Berzerk that draw on a lot of Western Fantasy tropes have this. I totally lost interest in the anime and the show every time it flashed back to that poof who becomes a god.
Now, I liked reading Dragonball, watching some of DBZ, and I liked Record of the Lodoss War. But, for some reasons I can't entirely articulate, the worldview, focus and characters in a lot of anime are completely uninteresting to me. This is also true of most television, most fantasy, and most movies. I have very specific and high standards, because I can always turn this shit off and go read one of the fantasy masterworks I haven't gotten around to - which will certainly be better.
I would like more anime if the characters had properly shaped heads, were mature adults, weren't targeted at horny teenage boys and faggots, and things were generally more gritty and coherent instead of 'for the sake of the plot, magic happens'. Basically, if it was western animation in the style of Robert E. Howard. I would also like more western animation if it removed all the stylized art, child protagonists, and nonsensical plots.