It's considered rude because it's considered rude. It's just part of general etiquette and there's no magical mystical sacred inscrutable reason for it.

It's like it's rude to walk down the

street while picking your nose, or spitting or peeing on the street is in the United States. Is there a magical mystical reason why picking your nose on the street is impolite in the U.S.? I don't think so.

(Incidentally, spitting and peeing (in a discreet corner, men only) on the street weren't considered that rude in Japan in earlier times, although these days they are. Only drunks and older men who don't care do either anymore. So much for Japanese people being the paragon of politeness huh.)

Every country or culture has its own rules of conduct, and usually they are there Just Because.

Also, it should be noted that eating or drinking while walking isn't considered to be that polite in many European countries either.

ETA: Eating or drinking while standing up, called tachigui (立ち食い)is very different from eating while walking. As long as you're standing and eating in a designated area it's fine. There are many stand-up eateries in Japan, most which serve quick and easy meals like udon, ramen, etc. Here's someone slurping a bowl of udon noodles at a tachigui udon stand located on a train platform.

Here's the tachigui corner of a famous 200-year old soba restaurant in Shinjuku. (They have seats and tables inside for people who prefer to eat sitting down.)

A tachigui sushi restaurant in Shinagawa station.