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

        char sexIndex = 'F'; //female (женский) пол для определения 3-его конструктора класса Cat

        String gDadName = r.readLine();
        Cat gDad = new Cat(gDadName);

        String gMomName = r.readLine();
        Cat gMom = new Cat(gMomName);

        String DadName = r.readLine();
        Cat Dad = new Cat(DadName, gDadName);

        String MomName = r.readLine();
        Cat Mom = new Cat(MomName, gMomName, sexIndex);

        String SonName = r.readLine();
        Cat Son = new Cat(SonName, MomName, DadName);

        String DghtName = r.readLine();
        Cat Dght = new Cat(DghtName, MomName, DadName);

        System.out.println(gDad);
        System.out.println(gMom);
        System.out.println(Dad);
        System.out.println(Mom);
        System.out.println(Son);
        System.out.println(Dght);
    }

    public static class Cat {
        private String name, gfparent, gmparent, fparent, mparent;
        public char sexIndex2 = 'f'; //female (женский) пол для определения 3-его конструктора

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

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

        Cat(String name, String gmparent, char sexIndex2) {
            this.name = name;
            this.gmparent = gmparent;
            this.sexIndex2 = sexIndex2;
        }

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

        @Override
        public String toString() {
            if (gfparent == null && gmparent == null && fparent == null && mparent == null)
                return "Cat name is " + name + ", no mother, no father";
            else if (gfparent == null && fparent == null && mparent == null)
                    return "Cat name is " + name + ", mother is " + gmparent + ", no father";
                else if (gmparent == null && fparent == null && mparent == null)
                        return "Cat name is " + name + ", no mother, father is " + gfparent;
                    else
                        return "Cat name is " + name + ", mother is " + mparent + ", father is " + fparent;
        }
    }
}
Код компилируется без проблем, но ругается на 5-ое и 6-ое условие. Может быть, забыл пробел или еще что-то, но вроде всё верно.