Final answer:
The Duke in 'My Last Duchess' was disgusted with the Duchess for her equal treatment of all pleasantries and her lack of appreciation for his aristocratic gift, leading to her tragic end.
Step-by-step explanation:
In Robert Browning's poem, My Last Duchess, the Duke is disgusted with his last duchess primarily because of her perceived disregard for the exclusivity and prestige of his attention and her supposed lack of discrimination in her pleasantries. The Duke describes how she would treat everything with the same level of delight, whether it was the sunset, a branch of cherries from an officious fool, or the Duke’s own favor, which he felt was far more valuable. This failure to distinguish between his 'gift of a nine-hundred-years-old name' and regular courtesies led the Duke to feel his pride wounded, ultimately becoming a significant factor in the Duchess' demise.