Shakespeare begins in Act I with Lady Macbeth's quote to her husband, "Look like the innocent flower, but be the serpent under it." She is calling him the serpent...a creature that from the beginning of time has been associated with fear, fangs, and death.
In Act II, all the earth rebels against the death of Duncan. Owls scream, crickets cry, horses break out of their stalls and eat each other.
In Act III, Macbeth also tells his wife, "Full of scorpions is my mind." Scorpions, like snakes, are not warm, fuzzy sorts of animals. You wouldn't want to cuddle with these creatures for their potential to do harm. It shows Macbeth's state of mind and his downward spiral. He also references Banquo and Fleance in terms of snakes--"We have scotched the snake but not killed it"--since they pose a threat to him and his throne.
In Act V Macbeth goes to his death "bearlike"...he makes references to being tied to the stake (bear-baiting, a popular public entertainment in Elizabethan times)...giving an otherwise honorable animal a more fierce and defensive backed up-into-a- corner attitude.
Unlike Macbeth, other characters are spoken of in terms of more honorable and admirable animals--hens, chicks, monkeys, cats, etc.
As Macbeth falls further and further into irreparable spiritual damage, the animal imagery he uses and that used to describe him is increasingly more threatening and dangerous.