Although Macbeth may seem to be fulfilling fate, as he fulfills the prophecies of the witches, his decisions are tragic and lead to his downfall.
The witches meet him and proclaim he will be Thane of Cawdor, and eventually King of Scotland. They also proclaim that his friend Banquo will father a line of Kings.
Later, Macbeth and Banquo rendezvous with King Duncan, and King Duncan declares Macbeth is Thane of Cawdor, with the discovery of treachery by the previous Thane. This convinces Macbeth that the prophecies of the witches are true. Shortly after that, King Duncan names his son Malcolm Prince of Cumberland, the heir to the Scottish Throne. Macbeth observes that this could prevent him from becoming King of Scotland.
Later in the play, King Duncan and his son Malcolm come to Macbeth's castle to visit. Rather than trust in fate to eliminate King Duncan and his sons, Macbeth murders King Duncan and frames Malcolm. This decision starts his downfall since he resorted to evil to fulfill the prophecy rather than trust fate.
With Duncan dead, and the Prince of Cumberland deposed for the murder, Macbeth becomes King as he already has two thanedoms. But then Macbeth remembers that it was prophecied that Banquo would father a line of Kings. This prophecy is ambiguous, it could mean Banquo's son would ascend to the throne, or it could be several generations until one of Banquo's descendants becomes King, and starts a dynasty. Macbeth furthers his downfall by assuming that the prophecy portends a threat to his reign, and sends assassins to kill Banquo and his son. He has begun to look like a tyrant instead of prudent King.
Later in the play, Macbeth visits the Witches and they tell him to beware of Macduff the Thane of Fife, that his reign will not end til' the woods come to Dunsinane Castle (the Throne of Scotland), and that he need not fear "a man of woman born." These prophecies are again ambiguous. Macduff poses a possible threat to his reign, the wood won't advance on Dunsinane in his lifetime (it will slowly advance but that takes centuries), and since all men are born of women Macbeth should die of natural causes. Macbeth orders Macduff and his family wiped out to destroy that threat to his reign and trusts that the other two prophecies are long term predictions.
But, Macduff escapes and reaches Malcolm in England. The witches prophecy meant Macbeth should leave Macduff alone, and since he didn't Macduff will now threaten his reign. Malcolm, Macduff, and a contingent of English soldiers march on Dunsinane Castle using boughs from the trees in the wood to hide their approach, so the wood came to Dunsinane. And then it turns out that Macduff was born by C-section so he was not "of woman born," and ultimately kills Macbeth.
Had Macbeth trusted fate, not feared Banquo's lineage, and left Macduff alone, his reign would have lasted, but his decisions on all of these conspired to undo him, resulting in a short tyrannical reign.