Oi, nobody said she's to marry her uncle. They only said her uncle's going to be the heir and she's out of the consideration even though her claim is legitimate.. read, people.
And translator, I think using "I cannot" doesn't necessarily mean anything deeper. I could mean something like "No matter what, I cannot bring myself to break the tradition", or to avoid displeasing someone of higher status by assigning agency to the situation instead of to himself.