Why are class members duplicated in the builder pattern?

The builder pattern (in Java) is usually illustrated by an example like this:

public class MyClass {

    private String member1;

    private String member2;

    // Getters & setters

    public class MyClassBuilder {

        private String nestedMember1;

        private String nestedMember2;

        public MyClassBuilder withMember1(String member1) {
            this.nestedMember1 = member1;
            return this;
        }

        public MyClassBuilder withMember2(String member2) {
            this.nestedMember1 = member1;
            return this;
        }

        public MyClass build() {
            MyClass myClass = new MyClass();

            myClass.member1 = nestedMember1;
            myClass.member2 = nestedMember2;

            return myClass;
        }

    }

}

So we get two very similar classes and since this pattern is mostly applied when we have a big number of members, we get a big amount of similarities. This violates the DRY principle in my opinion.

What is wrong with the following code?

public class MyClass {

    private String member1;

    private String member2;

    // Getters & setters

    public class MyClassBuilder {

        private MyClass myClass = new MyClass();

        public MyClassBuilder withMember1(String member1) {
            myClass.member1 = member1;
            return this;
        }

        public MyClassBuilder withMember2(String member2) {
            myClass.member2 = member1;
            return this;
        }

        public MyClass build() {
            return myClass;
        }

    }

}