Why `private static` field is not allowed in Java 8 interface?

Interfaces are not classes. They have no private state. Even a public logger in the interface is a design smell and an abuse of interfaces.

The use case for static fields in interfaces is mainly for compile-time constants, not for stateful objects.

In the pre-Java-8 view of the world, interfaces were purely for interface contracts, and private members exist purely for implementation, so this restriction was completely sensible.

In the post-Java-8 world, where interfaces can carry behavior (but not state), it starts to be reasonable to ask whether other features of classes should be applied to interfaces as well. (However, just because something might be "reasonable" doesn't mean it must be supported; there is often more than one reasonable way to construct the world.)

In Java 9, private methods in interfaces will be supported.