Is it the style? The action? The characters? All of the above? How about the creativity and originality of the stories. Sure, we all enjoy the action in a thrilling anime, or the way the creator captured the eyes of the main character's love interest. But for us, it is the stories. We can over look poorly animated characters with stick figures, especially when the story grabs you and draws you in.
We can enjoy a superbly animated fight scene, but more so if the story keeps you coming back for more.
We even enjoy the over the top, borderline R-rating harem anime with ridiculously top heavy female characters and the sex starved main character with a devotion to his harem, which only adds to the well thought out story.
This is what has us coming back over and over again. It is the one thing that animation, movies and television in the west is devoid of. Anime isn't used to push a political opinion or narrative, it's not trying to check all the boxes for it's diversity quota, it is an escape (albeit temporary) from the ups and downs life brings us. We love sharing our opinions and love of anime with others and we are a part of a larger community that enjoys a good story, even if it is silly, unbelievable or nonsensical.
It is the story we remember, it is the story that we can relate to, it is the story that moves us, even to tears sometimes.
If the anime doesn't have a good story, it's a struggle to watch. Some anime, unfortunately, are lacking in the story department, or had a great story and it gets derailed before the end, or lacks a proper ending. (Or one that leaves viewers satisfied)
So, this is what we love about anime. It's the story, and the storytellers. And yes, sometimes all the pieces fall into place and you come across the one anime you love, the story that never gets old, and the characters that break the mold.
Anime are tickling that part of our brains we can't itch or scratch. They are giving us that escape, that moment where we let down our defenses and enjoy the story without being preached to, or shamed or insulted. The moment we all look for, the moment we're entertained.
It is what the west, especially Hollywood and American television, has stopped giving to viewers, readers and listeners. The moment where we can get caught up in the story and have a reprieve from our lives and our problems. This is what makes anime special to us.