Why do you need a javascript reset constructor during inheritance?

Why is it important that I reset the constructor from Mammal to Cat? I played with this code and did not find any negative consequences of having the "wrong" constructor.

function Mammal(name){
    this.name=name;
    this.offspring=[];
}

Cat.prototype = new Mammal();        // Here where the inheritance occurs
Cat.prototype.constructor=Cat;       // Otherwise instances of Cat would have a constructor of Mammal

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

eg:

function Mammal(name){
    this.name=name;
    this.offspring=[];
}

Cat.prototype = new Mammal();        // Here where the inheritance occurs


function Cat(name){
    this.name=name;
    this.hasFur = true;
}

c1 = new Cat();
alert(c1.hasFur); //returns true;