Why do some people believe in The Matrix that the world is a dream world?

Because its a philosophical idea that the script writers have made into a movie.

the movie works on so many levels, but most people miss the philosophical possibilities of us actually living in the matrix too! - which is what I believe the creative scriptwriters are actually suggesting in the movie - its a clever idea.

As for why do they suggest this? well there is no way to know ultimately (until we 'meet our makers') and to argue for or against this is a 'moot' - like alot of philosophy is really if were honest.

People in the matrix movie dont believe that the world is a dream world in real life. They are what you call actors. Actors are people who pretend to do and believe in stuff. In other words, make believe. and they justdepend on what they think might be real they just really like the movie they think it's cool