In Macbeth, what arguments does Macbeth raise for not killing Duncan in Act I scene vii?
I take it you are referring to the soliloquy that Macbeth gives in Act I scene 7. This is a very important speech that Macbeth gives because in it he reveals something of his doubt and inner anguish about the act as he begins to have second thoughts. Initially, Macbeth starts off by talking about the best way to do it, saying that if it were done quickly, it might limit the possibilities for reprisals. Macbeth says that, for the glory that he could gain, he would "jump the life to come," as in risk the judgement that he might receive by committing the crime of regicide.
However, Macbeth still fears vengeance. He says that by killing Duncan he would teach "Bloody instructions" that "return / To plage th'inventor." Killing Duncan might find Macbeth himself killed out of revenge, which is of course precisely what happens. Then Macbeth goes on to talk about reasons why he shouldn't kill Duncan. Firstly he is Duncan's subject and secondly his host - Macbeth would break trust in a massive fashion were he to kill Duncan. He also says that Duncan has been such a pious and "meek" king that to kill him would surely bring eternal damnation. Lastly, he uses an unforgettable metaphor to describe his ambition:
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on th'other -
He says the only quality he can use to convince himself to kill Duncan is his ambition, which can be likened to someone who is to eager to ride and therefore jumps so hard and so high when mounting the horse they fall completely on the other side.
Thus Macbeth is concerned about a whole series of possible outcomes to committing murder, fearing both judgement in this world and in the world to come. Crucially, however, Lady Macbeth manages to persuade him in the rest of this scene in what must be one of the best examples of manipulation in literature.