What does "the milk of human kindness" mean?

Shakespeare seems to be doing his best to retain some modicum of audience sympathy for his tragic hero Macbeth by placing some of the blame for the murder of King Duncan upon Macbeth's ambitious and totally heartless wife. Scene 5 of Act I begins with a long soliloquy in which Lady Macbeth accuses her husband of being too full of the milk of human kindness. This hardly sounds like an accurate description of Macbeth, the man who specializes in killing other men in battle without mercy. Nevertheless, his wife should know him better than anyone. We are to understand that Macbeth's biggest problem in achieving the crown will be that he is too soft-hearted. Here is his wife's assessment.
Yet do I fear thy nature; It is too full o’ the milk of human kindness To catch the nearest way. Thou wouldst be great; Art not without ambition, but without The illness should attend it. What thou wouldst highly,That wouldst thou holily; wouldst not play false, And yet wouldst wrongly win. Thou'ldst have, great Glamis, That which cries, “Thus thou must do, if thou have it; And that which rather thou dost fear to do Than wishest should be undone.” Hie thee hither, That I may pour my spirits in thine ear, And chastise with the valor of my tongue All that impedes thee from the golden round, Which fate and metaphysical aid doth seem To have thee crown'd withal.
She does succeed in persuading her husband to commit the murder, but Shakespeare does a better job of making Macbeth appear to be a tyrant than in making him a sympathetic figure. Macbeth is full of the milk of human kindness, but nevertheless he sneaks into Duncan's chamber and kills the old man without wanting to do so. A short time later, he will kill Duncan's two guards mercilessly to prevent them from having any chance of protesting their innocence. We feel no pity for the mad tyrant when he meets his end.