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The third witch
Lady Macbeth echoes the words of the witches when she says "All hail, Macbeth, that shalt be king hereafter!". This echoes the witches' prophecy that Macbeth will become king.
Lady Macbeth says king Duncan resembles her father, so she encourages macbeth to murder him.
The Third Apparition
The Prophecy says Macbeth will be king. Duncan is king. Macbeth cannot be king while Duncan is king. Duncan will not be king when he is dead. Therefore, make Duncan dead.
Lady Macbeth thinks Macbeth will not achieve power because he will not kill the King who he shall become (says the witches first prophecies). When he eventually does, Lady Macbeth is proven wrong. So shame on herself!
he says that her castle is warm and welcoming and that he trusts her.
No. King Duncan was clueless. He admits it himself: "There's no art to find the mind's construction in the face; he was a gentleman in whom I built an absolute trust." He had no idea what was going on with Macbeth. Macbeth really expected to be named as Duncan's heir (he was after all a successful warrior unlike the feckless Malcolm) and was shocked and hurt when Duncan named Malcolm Prince of Cumberland. And then Duncan says "And now the party's at Macbeth's place!" He was, as I said, clueless.
Malcolm says on the battlefield, Macbeth's army has been delibertly missing them. It seems no one wishes for Macbeth to be king, not even his own side!
Macbeth hesitates to kill Duncan because he has a change of mind. He begins thinking about the fact that Duncan has recently honored him by promoting him to the position of Thane of Cawdor. Likewise he reflects that if you get power by violence you set an example for someone who wants to get rid of you. Also, the King is not only his king but also his cousin. And there is an ancient taboo against harming guests in your house. And besides, if it were ever known what he did, there would be a huge outcry because Duncan is such an agreeable old buffer. And against all of this, what can Macbeth think of to encourage him to kill Duncan? Just the chance of becoming king. Big deal.
Were to be king, god had to choose you, so in theory whatever the king does/ says god agrees and is behind it.
Quick, get some Duncan Donuts in!