In this excellent and rather chilling poem, we are presented with one side of a conversation where the speaker shows his audience a portrait of his last Duchess, and casually infers as if in passing how he disposed of her because of the interest she provoked in other men. As the poem ends we discover that the person he is talking to is actually an emmisary from a Count whose daughter the speaker is hoping to marry.
It is very important then, as your question indicates, to consider the attitudes expressed by the speaker in the poem. Note how he is presented as an incredibly proud man who obviously expects perfection in his belongings, including his wife:
...and if she let
Herself be lessoned so, nor plainly set
her wits to yours, forsooth, and made excuse,
--E'en then would be some stooping; and I choose
Never to stoop.
Notice the defiance and arrogance in his declaration that he chooses "never to stoop." It is also interesting as well to consider how the poem ends. Having passed the portrait of his last Duchess, the speaker draws his audience's attention to another object in his possession:
Notice Neptune, though,
Taming a seahorse, thought a rarity,
Which Claud of Innsburck cast in bronze for me!
The fact that Neptune is taming a seahorse clearly is significant and expresses his desire for complete mastery and his determination to "break in" his wives. The Duke is clearly trying to impress his guest but also show his expectation of perfection in all of his possessions--wives included.