Bugs Bunny is an alien and all Looney Tunes artists were under alien mind control when they animated Looney Tunes. There is no other explanation for how such intricate hand-drawn cartoons could be made. Normal humans not under mind control could never make these. Note that Bugs Bunny is never caught much like aliens are never caught by humans, they're always tricky and get away with technology that seems like magic.

He's not actually a rabbit even, he's just a furry alien much like bigfoot who manifested his existence on another dimension into the minds of humans to be made into a 2D cartoon to communicate with us one thing: Humor.