Lady Macbeth is the villain. Macbeth is, in fact, a tragic hero.
The first time I ever read Macbeth I was struck by the feeling of sympathy I had for the eponymous character at the end of the play. He had - surely - brought on his own downfall and demise and deserved his fate. Why the strange twinges of empathy for such a monster?
In fact, from the very beginning, Shakespeare sets Macbeth up not as an active protagonist, but as an instrument of fate.
The opening scenes of the play set Macbeth up as a person of great stature. He is a captain, honoured by the King and loved by his friends.
What he hath lost noble Macbeth hath won.
He is also honoured by the witches, although it is not clear whether or not this is in mockery. In any respect, the witches tell Macbeth he will gain further honour and titles.
This begs another open question: when the witches deliver their prophecies unto Macbeth, are they binding him to fate? Or are they corrupting him with promises, like devils tempting a mortal's weakness? Because it's clear that Macbeth's great weaknesses are pride and ambition. So the witches' words seem calculated to send Macbeth down the path to red ruin.
This is never answered, but that makes it at least a possibility that Macbeth is no longer in charge of his destiny. And even if he is, he's being manipulated by diabolical forces which are impossible for him to resist due to his character flaws. Either way, when his inevitable fall comes, we can see him sympathetically as a victim of circumstance as well as the tyrant and murderer he has become.
Contrast this with Lady Macbeth. She is described in much less glowing terms. In fact, at the end of the play, Malcolm says
Producing forth the cruel ministers
Of this dead butcher and his fiend-like queen,
Her behaviour, in contrast to Macbeth's, is purposefully callow. Macbeth initially does not want to kill the king - it is his wife who persuades him to do so. Note this is partly because she is impatient for the power and riches that it brings.
Glamis thou art, and Cawdor; and shalt be
What thou art promised: 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;
Impatience is a poor excuse for murder. Note also that she attempts to persuade Macbeth to do the deed in truly nefarious means – insulting her husband and claiming she herself would not hesitate to violently kill a child.
Which thou esteem'st the ornament of life,
And live a coward in thine own esteem,
I would, while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out, had I so sworn as you
Have done to this.
One could argue that she, too, is in the grip of evil magic and her actions are beyond her control. Evil spirits are invoked:
The raven himself is hoarse
That croaks the fatal entrance of Duncan
Under my battlements. Come, you spirits
That tend on mortal thoughts, unsex me here,
And fill me from the crown to the toe top-full
Of direst cruelty! make thick my blood;
But note a key difference. Macbeth met the witches either by chance or at their behest. His wife is deliberately inviting the devil to make her even more wicked than she already is. Every cruel choice she makes is of her own volition.
Eventually, of course, it catches up with her in her nightmares. And now the audience might feel a twinge of sympathy - yet it is clear she has brought this on herself, by choice. One of the many fascinating things about Macbeth, besides its open questions of fate and destiny, is how it shows us an unusually tender side to villainy in all its forms.