Why override Equals|GetHashcode|Operators

using System;
using System.Collections.Generic;
					
public class Program
{
	public static void Main()
	{
		var first = new ComparisonTestDefault() { 
			Id = 1, 
			Name = "teste" 
		};
		
		var second = new ComparisonTestObjectMethodsOverrided(){ 
			Id = 1, 
			Name = "teste" 
	 	};  
		
		//default output is the name of the type
		Console.WriteLine(first.ToString());
		
		//output will be the id and the name
		Console.WriteLine(second.ToString());
		
		//compare using hashcode/equals from objects
		var firstDict = new Dictionary<ComparisonTestDefault, int>(){
			{ new ComparisonTestDefault(){ Id = 1, Name = "1" }, 1 },
			{ new ComparisonTestDefault(){ Id = 2, Name = "2" }, 2 }
		};
		
		var secondDict = new Dictionary<ComparisonTestObjectMethodsOverrided, int>(){
			{ new ComparisonTestObjectMethodsOverrided(){ Id = 1, Name = "1" }, 1 },
			{ new ComparisonTestObjectMethodsOverrided(){ Id = 2, Name = "2" }, 2 }
		};
		
		var firstKeyFound = firstDict.ContainsKey(new ComparisonTestDefault(){ Id = 1, Name = "1" });
		var secondKeyFound = secondDict.ContainsKey(new ComparisonTestObjectMethodsOverrided(){ Id = 1, Name = "1" });
		
		//new object, can't be the inserted key (produces false)
		Console.WriteLine(firstKeyFound);
		
		//new object but with equals and gethashcode overwritten (produces true)
		Console.WriteLine(secondKeyFound);
		
		object a = null;
		object b = null;
		var c = new object();
		var d = new object();
		
		Console.WriteLine(ReferenceEquals(a,b));
		Console.WriteLine(ReferenceEquals(c,d));
		Console.WriteLine(ReferenceEquals(a,c));
		Console.WriteLine(ReferenceEquals(a,d));
		Console.WriteLine(ReferenceEquals(b,c));
		Console.WriteLine(ReferenceEquals(b,d));
	}
}

public class ComparisonTestDefault
{
	public int Id {get;set;}
	public string Name {get;set;}
}

public class ComparisonTestObjectMethodsOverrided
{
	public int Id {get;set;}
	public string Name {get;set;}
	
	public override string ToString(){
		return $"{Id}: {Name}";
	}
	
	public override int GetHashCode(){
		unchecked {
			//hash base with a big prime number to generate a overflow mixing the bits and producing a better hash distribution
			var hash = (int)2166136261;
			//this will produce the overflow
			var prime = 16777619;

			//xoring the hash and the prime will follow the FNV hash function algorithm
			//https://en.wikipedia.org/wiki/Fowler%E2%80%93Noll%E2%80%93Vo_hash_function
			hash = (hash * prime) ^ Id.GetHashCode();
			hash = (hash * prime) ^ Name.GetHashCode();
			
			return hash;
		}		
	}
	
	public override bool Equals(object value)
	{
		var obj = value as ComparisonTestObjectMethodsOverrided;
		
		//if the compared value is not "referentially" the same as null (a.Equals(null))
		return !ReferenceEquals(null, obj)
			&& string.Equals(Name, obj.Name)
			&& Equals(Id, obj.Id);
	}
}

/*

ComparisonTestDefault
1: teste
False
True
True
False
False
False
False
False

*/