So many reasons. Firstly, I like animation. It can present a story in a fascinating array of colours, and contrasts, and variations. It is not bound to what is achievable with live-action special effects or costumes. I find alot of anime visually attractive. Compared to live action, it both makes things clear and leaves things to the imagination. Bearing that in mind, I used to watch Western animation. However, Western animated shows are set in much less believable environments, often with little attention to lucid visuals. Anime bridges that gap as it provides a medium for those who want more visually mature animation. Compare Death Note to the Simpsons. How much detail do you think they put into a single scene of Death Note, compared to a whole Simpsons episode? Though that may be a nefarious comparison and I may be underestimating the effort put into The Simpsons' animation. Also there are plenty of anime which have weak visuals.
Which brings me to another reason. There is a massive variation of storylines within anime. They are not bound by mundane details such as audience sensibilities or special effects budgets. Anime/manga is not afraid to touch topics which would otherwise be too controversial or too wacky for Western audiences. Imagine the outrage, say, if Battle Royale, Berserk, or Death Note had been screened alongside the Simpsons or Family Guy. Japanese studios produce animation for all audiences. It is not just a child or family thing.
In conclusion, Japanese animation appeals to my demand for animation which Western Animation generally doesn't. I have other reasons, but those are particularly important.