The fact that the character is unbelievable does not allow Macbeth to meet this requirement of a tragedy.
When further examining Macbeth as a "tragic hero", you must determine whether the hero is a man who is predominately good, but has faults. According to Aristotle, this means that the character cannot be completely good because then his downfall would be unfair and cannot be completely evil because then the characters downfall could be perceived as a punishment. Macbeth is clearly portrayed throughout the work as a purely evil character. He murders without thinking including innocent women and children. His downfall because of his horrendous actions almost seems deserved. There is no feeling of catharsis for Macbeth, which is the next requirement for a tragedy. Catharsis or the downfall of the character and his ensuing suffering must create a feeling of empathy in us which allows us to be devoid to the dangerous emotions the character suffers from. When Macbeth suffers there is no feeling of empathy towards him because he is so evil.
According to Aristotle, the "tragic hero" must experience his ill fortune, not as punishment, but as a mistake or a flaw in his personal character. Macbeth's fate, which he hears from the three witches, drives him to greed, drastically increases his lust for power and eventually gives him a feeling of invincibility. This desire for power is Macbeth's tragic flaw. When the witches tell him his fate Macbeth responds by only taking heed to the visions of power that the witches show him and not paying attention to the witches mention of misery ahead for Macbeth. This is told to Macbeth by the second witch comparing Banquo and Macbeth saying, "Not so happy, yet much happier". Macbeth does have an obvious tragic flaw, which means that in this are Macbeth does fit the requirement of a tragedy.
Macbeth also fits another requirement without contest. Reversal or the process by which a hero must start out with honor and reputation, recognized as a morally good man and through the events of the play must lead to his eventual downfall and likely the loss of his life.