What do you like about anime?
For me I enjoy the general artstyle for one thing. The large eyes are interesting to look at, and it does feel like they are able to show a huge spectrum of emotion from characters. Many of them are emotions I haven't seen from other animations with smaller/cartoonish eye drawings. It is easy to really get a feel for the emotions the characters go through due to how the eyes and facial expressions of many anime & manga characters are drawn.
The biggest thing in general that I like is how there is a lot of anime that exists with more mature and deep stories compared to other forms of animation. There are anime geared for teenagers, young adults, and even older adults as well. I'm able to think more deeply about the characters and story from within the anime and follow a concrete story. Anime such as Psycho-Pass, Higurashi, Death Note, and Yona of the Dawn are examples of anime where the characters and story require one to think deeply about it and analyze it. Because you also watch the journey of characters from the beginning, it is easy to get attached to them as well.
I first got into anime when I was around 12 or 13. It appealed to me since I was at a point where I was getting tired of a majority of western animation since most of it was mostly comedy with not a whole lot of deep thinking behind it. (There were a few exceptions naturally such as Avatar: The Last Airbender for example) That was when my transition period began. A show called Code Lyoko is also something I got into around that time. It is an animation from France that you may/may not have heard of. While it isn't an anime, it was a show where the tone and characters felt more serious compared to most of the things I watched before. X.A.N.A the rogue Artificial Intelligence from the show truly felt like a very intimidating threat for the characters to deal with throughout the show.
A side effect of watching a lot of anime overtime was that I grew comfortable watching with subtitles and in combination with a Japanese class I took during college, I understand a degree of Japanese. I'm not fluent in it, but I do have a basic understanding of the grammar, and what a fair amount of words mean.
To summarize it, it is certainly the more mature or complex feeling from anime that got me attracted to it as a whole. Western animation is mostly geared towards a younger audience. While it is absolutely fine for other people to still watch and enjoy it as they get older, it isn't something I enjoy anymore. Anime has shown me that it is still possible to have animation with a tone set for an older audience, without coming off as forced. Hopefully that makes sense, I had to take a few paragraphs to sort out my thoughts.