Micro servidor nodejs para get e post usando somente http nativo do nodejs

gistfile1.txt

var http = require('http');
var url = require('url');
var querystring = require('querystring');

var contatos = [
	{nome: "Bruno", telefone: "9999-2222", data: new Date(), operadora: {nome: "Oi", codigo: 14, categoria: "Celular"}},
	{nome: "Sandra", telefone: "9999-3333", data: new Date(), operadora: {nome: "Vivo", codigo: 15, categoria: "Celular"}},
	{nome: "Mariana", telefone: "9999-9999", data: new Date(), operadora: {nome: "Tim", codigo: 41, categoria: "Celular"}}
];
var operadoras = [
	{nome: "Oi", codigo: 14, categoria: "Celular", preco: 2},
	{nome: "Vivo", codigo: 15, categoria: "Celular", preco: 1},
	{nome: "Tim", codigo: 41, categoria: "Celular", preco: 3},
	{nome: "GVT", codigo: 25, categoria: "Fixo", preco: 1},
	{nome: "Embratel", codigo: 21, categoria: "Fixo", preco: 2}
];

var headers = {};
    headers["Access-Control-Allow-Origin"] = "*";
    headers["Access-Control-Allow-Methods"] = "POST, GET, PUT, DELETE, OPTIONS";
    headers["Access-Control-Allow-Credentials"] = true;
    headers["Access-Control-Max-Age"] = '86400'; // 24 hours
    headers["Access-Control-Allow-Headers"] = "X-Requested-With, Access-Control-Allow-Origin, X-HTTP-Method-Override, Content-Type, Authorization, Accept";

http.createServer(function (req, res) {

    var url_parts = url.parse(req.url);
    switch(url_parts.pathname) {

    case '/contatos':
				res.setHeader('Access-Control-Allow-Origin', '*');
				//res.header('Access-Control-Allow-Methods', 'PUT, GET, POST, DELETE, OPTIONS');
				//res.header('Access-Control-Allow-Headers', 'Content-Type');
        res.writeHead(200, {'content-Type': 'application/json'});
        res.end(JSON.stringify(contatos));
        break;
    case '/operadoras':
				res.setHeader('Access-Control-Allow-Origin', '*');
				res.setHeader('Access-Control-Allow-Methods', 'PUT, GET, POST, DELETE, OPTIONS');
				res.setHeader('Access-Control-Allow-Headers', 'Content-Type');
        res.writeHead(200, {'content-Type': 'application/json'});
        res.end(JSON.stringify(operadoras));
        break;
    case '/contatos/inserir':
				var queryData = '';
				req.on('data', function(data) {
            queryData += data;
        });
        req.on('end', function() {
            var obj = querystring.parse(queryData);
            contatos.push(obj);
            console.log(req.socket._events.end);
						
        res.writeHead(200, headers);
        res.end('Objeto inserido.');
        });
    default:
        res.writeHead(400, {'Content-Type' : 'application/json'});
        res.end('Rota não encontrada');
    }
}).listen(3000, function () {
    console.log('server run on 3000');
});

case '/contatos/inserir':
var queryData = '';
req.on('data', function(data) {
queryData += data;
});
req.on('end', function() {
var obj = querystring.parse(queryData);
contatos.push(obj);
console.log(req.socket._events.end);
res.setHeader('Access-Control-Allow-Origin', '*');
res.setHeader("Access-Control-Allow-Headers", "Origin, X-Requested-With, Content-Type, Accept")
res.writeHead(200, {'Content-Type' : 'application/json'});
res.end('Objeto inserido.');
});

Error: h

OPTIONS
XHR
http://localhost:3000/contatos/inserir [HTTP/1.1 400 Bad Request 2ms]
Cross-Origin Request Blocked: The Same Origin Policy disallows reading the remote resource at http://localhost:3000/contatos/inserir. (Reason: CORS header 'Access-Control-Allow-Origin' missing).

Vi sua dúvida no grupo do Be MEAN.
Já tentou fazer assim:

app.all('', function(req, res, next) {
res.header('Access-Control-Allow-Origin', '');
res.header('Access-Control-Allow-Methods', 'PUT, GET, POST, DELETE, OPTION S');
res.header('Access-Control-Allow-Headers', 'Content-Type');
next();
});

Mas desse jeito seria usando express? isso?