You need to use bind in your class's constructor with the ES6 class method. In essence, arrow functions do this for you automatically.
constructor(props) {
super(props);
this.onSubmit = this.onSubmit.bind(this);
}
The more important thing to note here is that I believe the arrow function here will be created on each instance of the class, where the ES6 class method will be made part of the class's prototype and shared amongst all instances.