I think the idea behind it is that because the state is so powerful and has so many resources to turn to it is considered unfair to make a person testify in their own case. e.g The state should be able to convict you without having to rely on you tripping up on your own testimony!
5th Amendment applies in U.S. Courts and refers to the U.S. Constitution.
Under Irish Law he who asserts must prove. There is no onus on an accused to give evdience in a prosecution against himself.
Its not a law as such but a legal principle.