I am convinced, no matter how much wannabe-anime style art I've seen, that one has to at least have some Asian in them to draw the anime/manga style.  Yes, it's also cultural, but culture and genes go hand in hand.  The "L/R" misconception is actually the ear and brain processing the letters a certain way, and Japanese people are also more responsive to higher pitched sounds rather than low bass, as seen in a lot of their music.  So call me a eugenics Nazi, I don't care.

Most US or Europe art tends to have square or straight eyes, to denote seriousness or "toughness."  The anime round eye style seems to be a perception of femininity, a welcoming of it even in males, that allows the character to look naturally gentle or naive.  The sense of 2D moving fluidly in 3D is also different in some way.  US animators tend to focus on the whole body at once, from disney to Hanna Barbera to South Park to any show made for Adult Swim.

The closest thing to anime art is Pinup girls of the mid twentieth century (when females could be oggled without complaint) and some US comics, especially Image, but even these aren't pure manga style (they are unique, but some try to resemble anime). 

There is some perception of what a character "should" look like to manga artists, which creates the style, and can be seen in Korean anime style art where the heads are wider or more squished.  Somehow, the us perception of what a charracter should look like in 2D either ends up very two dimensional, or like Furry art.  Something in US artists makes a lot of them predisposed to drawing Furry art, or cartoon animals, but not humans.  Humans have always been the most awkward, strangest things to draw, and either must look photorealistic as in fantasy art, or be abstract and cartoony.