Anyone have any theories why Violet believed more in Edith than Robert and Cora? What makes Violet more hopeful when her parents are not? Interestingly, Violet is closest to Mary out of three granddaughters, but doesn't play favorites. We see her supporting all three of her granddaughters.
From the beginning, it's made clear that Robert and Cora don't think Edith has a chance at getting married. That no man will want her. From season 1-3, Cora belittles Edith and Robert ignores her. Only Violet gives Edith any voice of confidence. It is Violet who is the most upset with the idea of Edith marrying Sir Anthony. Robert and Cora don't like it, but are not as upset with it as much as Violet. Ultimately, they don't think Edith can do better than being "an old man's drudge". This is why Robert and Cora give in, rather than reassure Edith that she can do better.
Season 1:
Robert and Cora's Bedroom:
Robert: We never talk about Edith.
Cora: I'm afraid Edith will be the one to take care of us in our old age.
Robert: What a gastly prospect.
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Mary's Bedroom:
Cora: You mustn't be so unkind. She (Edith) has less advantages than you.
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On the stairs after Sybil's first season. Cora congratulates Sybil and calls her a success.
Edith: You never say that to me.
Cora: I don't? Good job.
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Season 2:
Edith is arranging the presents for Matthew and Lavinia's wedding.
Violet: Your time will come.
Edith: Will it? Isn't this what spinsters do? Arrange presents for their prettier relations.
Violet: Don't be so defeatist dear. It's very middle class.
Season 3:
Robert: Out of the three of them, he (Sir Anthony) is the most traditional choice.
Violet: Robert, Edith is beginning her life as an old man's drudge. I shouldn't think a drawing room is much compensation for it.