form_3.js

//...state...
  addCat = (e) => {
    this.setState((prevState) => ({
      cats: [...prevState.cats, {name:"", age:""}],
    }));
  }
handleSubmit = (e) => { e.preventDefault() }
render() {
    let {cats} = this.state
    return (
      <form onSubmit={this.handleSubmit}>
        <label htmlFor="name">Owner</label> 
        <input type="text" name="owner" id="owner" />
        <label htmlFor="description">Description</label> 
        <input type="text" name="description" id="description" />
        <button onClick={this.addCat}>Add new cat</button>
//...rest of render...