I have mixed feeling on anime and manga. I appreciate it as a medium that doesn't restrict itself in the way animation and comics often do in America. Anime and manga aren't afraid to tackle adult subjects and present themselves as adult works because they see themselves as a medium whereas here in American cartoons and comics (though there has been a shift in the past two decades that has been working to remove this stigma) tend to be seen as strictly genres for kids.
On the other hand, I don't like the character designs that a lot of anime/manga uses. I can't watch/read stuff like Sailor Moon or Code Geass because I can't get over the way they draw people. It's particularly something about the way the faces are drawn, particularly the eyes and curvature of the face. It's just unappealing to me. I think for me the stereotypical anime style uses weird proportions for their characters that just fall into the uncanny valley for me.
I do like some art styles used in anime. The Studio Ghibli style is very appealing to me. I love their softly detailed characters and their stunning backgrounds. I enjoy works like Ghost in the Shell and Akira for their extremely realistic looking people and character proportions. I even enjoy watching Dragon Ball and Naruto (though I have several critiques regarding the stories of both) because they use character designs and styles unlike a lot of typical anime/manga which makes it enjoyable to look at for me. I'm not saying a character design needs realistic proportions or features, but the style that a lot of iconic manga/anime uses is just not pleasant for me.
This complaint is largely decreasing for me as the anime/manga art styles that I dislike are currently being used less and less in more modern works. The style has largely been in decline since the early 2000s and while I know that probably saddens some people the art style just doesn't work for me so I'm not bemoaned to see it's use in decline.
That being said, another trait of anime/manga that I don't like is that their portrayal of women. Naruto was my first instance of being exposed to the somewhat harsh treatment of female characters in anime/manga who are often relegated solely to side roles to serve the main protagonists. But then I discovered the outright exploitative nature of how many animes/mangas delve into fan service and sexual exploitation of their female characters. (Yeah occasionally a male will occasionally get a somewhat similar treatment, but that's rare and generally reserved for series which satirically poke fun at anime tropes.)
Finally, despite professing that I enjoy the art styles of Naruto and Dragon Ball, a lot of the stereotypes and tropes in these series (particularly shonen) bother me to no end. I do have a bit of a fondness for Naruto and Dragon Ball because they were my "gateway" animes and I do adore the abridged series by Team Four Star and Little Kuriboh (at this point I consider the TFS abridged to be the official dub of Dragon Ball Z, for me anyway). Still, if I discovered a series today that was similar to Naruto or Dragon Ball I'm not sure I could get into it in the same way.
So, long story short: I like anime/manga, but I'm picky. A lot of art styles, tropes, and fan service bother me; but I do enjoy many series and love how the stigma of animation/comics being for kids does not exist in it.