Я посмотрел в других ветках, люди решили её намного проще, используя меньше конструкторов. Так почему мы здесь можем использовать меньше конструкторов?
package com.javarush.task.task06.task0621;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/*
Родственные связи кошек
*/

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        String grandFatherName = reader.readLine();
        String grandMotherName = reader.readLine();
        String fatherName = reader.readLine();
        String motherName = reader.readLine();
        String sonName = reader.readLine();
        String daughterName = reader.readLine();

        Cat catGrandFather = new Cat(grandFatherName);
        Cat catGrandMother = new Cat(grandMotherName, catGrandFather);
        Cat catFather = new Cat(fatherName, catGrandFather, catGrandMother);
        Cat catMother = new Cat(motherName,catGrandFather, catGrandMother, catFather);
        Cat catSon = new Cat(sonName,catGrandFather, catGrandMother, catFather, catMother);
        Cat catDaughter = new Cat(daughterName,catGrandFather, catGrandMother, catFather, catMother, catSon);



        System.out.println(catGrandFather);
        System.out.println(catGrandMother);
        System.out.println(catFather);
        System.out.println(catMother);
        System.out.println(catSon);
        System.out.println(catDaughter);
    }

    public static class Cat {
        private String name;
        private Cat grandMother;
        private Cat grandFather;
        private Cat father;
        private Cat mother;
        private Cat son;
        private Cat daughter;


        Cat(String name) {
            this.name = name;
        }


        Cat(String name, Cat grandFather) {
            this.name = name;
            this.grandFather = grandFather;
        }

        Cat(String name, Cat grandFather, Cat grandMother) {
            this.name = name;
            this.grandFather = grandFather;
            this.grandMother = grandMother;

        }

        Cat(String name, Cat grandFather, Cat grandMother, Cat father) {
            this.name = name;
            this.grandFather = grandFather;
            this.grandMother = grandMother;
            this.father = father;
        }

        Cat(String name, Cat grandFather, Cat grandMother, Cat father, Cat mother) {
            this.name = name;
            this.grandFather = grandFather;
            this.grandMother = grandMother;
            this.father = father;
            this.mother = mother;
        }

        Cat(String name,Cat grandFather, Cat grandMother, Cat father, Cat mother, Cat son) {
            this.name = name;
            this.grandFather = grandFather;
            this.grandMother = grandMother;
            this.father = father;
            this.mother = mother;
            this.son = son;

        }

         Cat(String name,Cat grandFather, Cat grandMother, Cat father, Cat mother, Cat son, Cat daughter) {
            this.name = name;
            this.grandFather = grandFather;
            this.grandMother = grandMother;
            this.father = father;
            this.mother = mother;
            this.son = son;
            this.daughter = daughter;
        }


        @Override
        public String toString() {

            if (mother!=null)
            return "The cat's name is " + name + ", mother is " +mother.name+ " father is "+father.name;
            else if (grandMother!=null&&father!=null)
            return "The cat's name is " + name + ", mother is " +grandMother.name+ ", no father";
            else if (grandMother!=null)
            return "The cat's name is " + name + ", no mother, father is " +grandFather.name;
            else
            return "The cat's name is " + name + ", no mother, no father ";
            /*
            else if (grandMother != null&&grandFather != null&& son==null && daughter==null)
            return "The cat's name is " + name + ", mother is " +grandMother.name+ " father is "+grandFather.name;
            else if (mother != null&&father != null)
            return "The cat's name is " + name + ", mother is " +mother.name+ " father is "+father.name;
            */

            /*
            if (grandMother == null)
                return "The cat's name is " + name + ", no mother ";
            else
                return "The cat's name is " + name + ", mother is " + grandMother.name;
            */
        }
    }

}