I think you would have to say that Macbeth's demise was caused by fate. In the beginning, he takes control of the battle and because of his violent and brutal manner of killing, he is given the title of Cawdor. As a result of this, he seeks higher rankings sooner than he normally would.
However, when he runs into the witches before he knows of his new title, their suggestion that he will be king gets him started in his thinking. The witches are responsible for putting the idea in his mind. Before he met with them, he was just doing his job as Thane of Glamis. If he had not run into them, he would have been told by the King that he was now Thane of Cawdor as well, but he may not have immediately latched onto the idea of being king.
As a character in a tragedy, Macbeth is doomed to have a fatal flaw: his vaulting ambition. The witches state in Act 1 scene 1 that they plan to meet Macbeth with their duplicitous prophesies. As a loyal soldier he has never contemplated a crime as serious as regicide, but he has always been a killer. His prowess in battle and execution of the enemy is the reason for his first reward as Thane of Cawdor. Macbeth is a killer, fated to be so and fated to continue to be so, all that changes is in whose name he commits the deed.
In another of Shakespeare's plays, Julius Caesar, Cassius tells Brutus,
Men at some time are masters of their fates:
The fault, dear Brutus, is not in our stars,
But in ourselves that we are underlings (1.2)
Certainly, these words appy to Macbeth, who, despite the advice of Banquo, is tempted by the prophesies of the three witches. And, once he has done so, like the speaker of Frost's poem, "The Road not Taken," "way leads on to way." In his "vaulting ambition," he kills Duncan so that he can become king. And, his murderous path which leads to his act of killing Banquo then, in turn, leads to his being known as a tyrant by the other Scottish lords. Consequently, Malcolm solicits the aid of the English in ridding Scotland of this tyrant. And, as a further result of Macbeth's bloody deeds--not fate--Malcolm, who was not "born of woman" and the other Scottish lords who disguise themselves with the brush of Birnam Woods, move on the castle at Dunsinane and kill Macbeth, who has created his own fate by becoming so wicked:
I have lived long enough. My way of life
Is fall'n into the sear, the yellow leaf,
And that which should accompany old age,
As honor, love, obedience, troops of friends,
I must not look to have; but, in their stead,
Curses not loud but deep, mouth-honor, breath,
Which the poor heart would fain deny, and dare not. (5.3)
I agree that Macbeth had free will and that killing Duncan and Banquo and Macduff's family was all his own doing. However, he seems to be a pawn of fate to some extent. Clearly, the second set of prophecies comes true not without Macbeth really helping them along. It wasn't Macbeth who had an army camouflage themselves in branches from Birnam Wood. Macbeth didn't cause Macduff to have been born the way he was. So those prophecies do come true without Macbeth's help and they seem to indicate that his fate might have been preordained.
Macbeth, because he is a human being, has free will according to the religious convictions of the time. You might consider the following:
The witches made suggestions and predictions, but these are in no way forced upon Macbeth. He chose to "hurry" the prophesy instead of letting it happen on its own.
Macbeth clearly understands that he has this choice in his arguments against murdering Duncan. In Act I, scene 7 he states
...But in these cases/We still have judgment here...
...I have no spur/to prick the sides of my intent, but only/vaulting ambition...
Free will... 1) The witches predict his future but not how his becoming king is achieved 2) at no point was Macbeth forced into murdering any of his victims