1. Anime is only for kids
In Japan anime is created for all ages and there's plenty of anime aimed at adults in a variety of genres.
2. Adults only like anime for the fanservice
Being an otaku myself, and having been friends with several anime fans, I've never known anyone who only watches anime for the fanservice. Anime has a lot to offer and often has stories and comedic scenarios you would never get a chance to see in American tv. The extra fanservice is just an added bonus.
3. Actual Japanese high schools aren't like the ones in anime
Japanese society is a lot stricter than shown in anime, and real Japanese high schools aren't as glamorous.
4. They're not any different from American cartoons
Anime is made for all ages and unlike a lot of cartoons, have a much more complex and plot and art.
5. All anime are alike and I don't fit in that niche
Like I've mentioned before, there's soo many types of anime: sports, music, cooking, psychology, any hobby or subject you enjoy has an anime about it as long as you take the time to find it.
6. Anime is too weird for me
Unique characters and strange plots are what make stories exciting. Instead of looking for the mundane character thats just like you, watching a variety of weird characters interact in a new setting is what makes stories worth knowing.