"She is the woman whom I hate."
Translation:Benim nefret ettiğim kadın o.
Very good question. It's because we don't use cases with relative clauses.
"Benim nefret ettiğim kadından o." would mean "That is from the woman who I hate." As you see it means a whole different thing so there is no way to use it like this. That's why we ignore cases in subordinate (relative) clauses.
However if you really want you could say "Benim kendisinden nefret ettiğim kadın o." It means the same thing yet sounds more clear. You can use this structure only with people, not with objects.
Ektoraskan I love your simple explanations! ;)
The problem with my sentence is the present continuous tense suffix -yor. Tense suffixes are not used with -idIk at all. This object participle is used only for the present or past tense and the actual tense is deduced from the context.