His main argument, in his famous 'To be or not to be' speech, is basically that he is afraid of what may come after death 'The dread of something after death.' He thinks of death as an 'undiscovered country' from which nobody comes back to tell you about it (though in fact in an earlier scene the Ghost has suggested that there are horrors to be faced). Ultimately Hamlet can't find one positive reason for living - only the fear of death.
