Well, when I was a kid I was watching Pokémon on TV, but I didn't know what anime and manga were back then. Heck, I didn't know Japan existed, I was that young. I got into the show because I already liked the game.
I didn't know what anime was until my older cousin showed me Naruto. That led me to watching various others, most importantly Pita Ten and Saru Getchu (Ape Escape)'s anime. The story in various anime I watched caught my eye because they were less episodic than some of the stuff I had available in TV and interested me more. Basically I felt like a "big kid" or something watching them because they had a different tone than the cartoons I watched before. During that time I was your average weeaboo kid who wanted to make an anime when I grew up, and move to Japan and marry a Japanese man. I was one of those weebs who thought I should've been born Japanese just because I liked some of their cartoons, Vocaloid, and Touhou. I tried to draw things with the screen paused, it was a major inspiration in getting me to take drawing more seriously because I wanted to make it look good. Heck, during the younger part of that phase I thought anime people were actually real in Japan (keep in mind, I was like 7, I was dumb back then), but that could've a side effect of my imagination being very strong all of my life. I was the type of kid to make various fictional characters my imaginary friends. And yes, I did try to learn Japanese by watching anime and looking up random words despite not understanding things like their grammer, sentence order, or really anything vital, and in the end I was too lazy to commit to it. I was just a kid, after all.
Nowadays, while I have a ton of a respect for Japanese culture, I'm not a weeaboo. I'm now a cringey NoticemeDoitsuphile Germanophile. :3 My interest in anime and manga lies in multiple things. Firstly, while obviously not every artist looks the same, the art styles and expression are something that draws me in. Secondly, the stories and writing. There are multiple western comics and animated series, movies, and shows that have good stories I enjoy as wepl, but when it comes from a different part of the world, a different culture, I'm more likely to see concepts I never thought of brought up, or different ways of looking at them. I like seeing how good writing and clever visuals can collaborate to tell a compelling story. Also, yanderes are a thing.