Jim, the protagonist of the novel, loses his own father early on in the story so it could be said that he is thereafter on the look-out for a substitute father-figure. Although Silver is a villain, at first Jim does not really suspect that he is anything more than a ship's cook and he is so charismatic and affable that the boy warms to him and looks up to him. Even later on when Silver's true nature comes to light Jim retains some admiration for him.
Dr Livesey is the more acceptable and conventional father figure; it is to him that Jim turns after accidentally finding out about Silver's intended mutiny.
These two characters can be viewed as competing father-figures to Jim; it is the socially respectable Livesey that wins out.