Why do people worship false gods?

One Jehovah's Witness' View:Because Satan (the father of lies) directs them to! Read about it in the bible or talk to Jehovah's Witnesses.

Another View:

What gives you the right to claim their gods as false? To them, your religion is faulty... It is simply how they were raised.

What is true for you is not true for everyone else in the world. Nobody can really know with certainty which gods are false. Everyone should think for themselves not be propagandized. They should also respect the rights of others to believe as they wish.

Wikipedia says:

In some monotheistic religious denominations, the deities of pagan religions -- as well as other competing entities or objects to which particular importance is attributed -- are often called false gods. Conversely, polytheistic pagans may regard the gods of various monotheistic religions as "false gods" because they do not believe that any real deity possesses the properties ascribed by monotheists to their sole deity. Atheists, who do not believe in any deities, do not usually use the term "false god" even though that would encompass all deities from the atheist viewpoint.

Followers of each of the religions described above worship their God or gods because they really believe the God or gods exist. No other reason is required.