What prevents me from using a some server’s public key and impersonate another server [duplicate]

I read alot regarding RSA encryption/DH key exchange/digital signatures and the whole TLS protocol.

There’s something i am missing regarding the public key signatue validation.

Let say some website has a certificate signed with its private key, as a client I have access to the public key.

But if the server only sends the public key to the client, what is preventing me as an attacker from taking this public key, and returning it to who ever wants to communicate with me.

I mean, where is the private-key authentiction comes to place?

I created this small C# code to demostrate:

private const int _port = 4455; static void Main(string[] args) {     Task.Run(async () =>     {         await TcpServerInit();     });      Task.Run(async () =>     {         await TcpClientInit();     });      Console.ReadLine(); }  private static async Task TcpServerInit() {     var server = new TcpListener(IPAddress.Any, _port);     server.Start();      while (true)     {         TcpClient client = await server.AcceptTcpClientAsync();         using (var netStream = client.GetStream())         {             ServicePointManager.ServerCertificateValidationCallback = ValidateCertificate;             ServicePointManager.Expect100Continue = true;              using (var ssl = new SslStream(netStream, false))             {                 using (var cert = new X509Certificate2(@"MyPublicCert.cer"))                 {                     await ssl.AuthenticateAsServerAsync(cert, false, SslProtocols.Tls12, true);                 }             }         }     } }  private static async Task TcpClientInit() {     using (TcpClient client = new TcpClient("localhost", _port))     {         using (SslStream sslStream = new SslStream(client.GetStream(), false, new RemoteCertificateValidationCallback(ValidateCertificate), null))         {             var servername = "CN=localhost";             await sslStream.AuthenticateAsClientAsync(servername);             byte[] messsage = Encoding.UTF8.GetBytes("Hello");             sslStream.Write(messsage);             sslStream.Flush();          }     } }    private static bool ValidateCertificate(object sender, X509Certificate certificate, X509Chain chain, SslPolicyErrors sslPolicyErrors) {     //cert validation     return true; }