I don't know if you're still as confused as you were when you wrote this, but you were most likely thinking of modal logic when you talked of worlds in terms of defining properties like "having a parallel world". Modal logic is confusing to the philosophers who use it, and quite probably entirely useless. Many-worlds is about interpreting the Schrödinger wavefunction as the universe (and locating ourselves as tiny patterns concealed in various corners of it), not about verbal descriptions of worlds. Does that help explain the disagreement?