Why is Hecate angry? What is "mortals' chiefest enemy"?
Hecate is the head of the witches. She is angry because the witches have made prophecies to Macbeth without telling her. We learn she is the witch with the power—"the mistress of your charms"—and that she expects the other witches to work closely with her. She is also angry that they are interacting with Macbeth, who she says is "spiteful and wrathful" and out for himself. He, like most humans, she says, is not likely to do anything for them.
Hecate's speech is important because we learn that despite the faith Macbeth and Lady Macbeth invest in the prophecies of the three weird sisters, they are, ironically, not the ones with the real power. Second, her speech hints that the witches are looking for something in return for offering their prophecies. Finally, it is not until Hecate intervenes that Macbeth's fate is sealed.
The chief enemy of mortals, according to Hecate, is "security," by which she means false confidence that fate is on their side. She will build up this sense of "security" and use it against Macbeth.
Hecate first appears in the play in Act III, Scene 5. She is the goddess of the witches and she is angry at them. The reason for her anger is that they did not ask her if it was alright before they started to get involved with Macbeth. She thinks that he has used them for his own purposes.
Hecate says that the "chiefest enemy" of mortal people is security. The context for that is she is talking about how she's going to lure Macbeth into doing something stupid. She thinks he'll fall for it because he is ambitious and because people always want more than they have -- they hate being secure and content with what they have.