Why can't you override fields?

I think one reason is that override is for methods, which properties have (as accessors) and fields don't, so methods can extend overridden methods from base classes by calling them through the base object. Would we ever extend field values or just replace them? Redefining the field without override, however, only hides the inherited field, which means it still gets accessed in ways the programmer may not want, unless access were controlled through properties. Language design is filled with arbitrary choices that aren't necessarily logical. The language designers may have felt fields should focus on binding data to class instances, and properties should focus on directing access (including overrides).

Fields are intrinsically private and properties are public. You can only access properties outside of the immediate class and override them. Since fields are private and can't be accessed outside of the class they were declared in, there is no way to override them.