To aid in debugging, try temporarily switching to MailKit and using a code snippet such as the following:
using System;
using MailKit.Net.Smtp;
using MailKit.Security;
using MailKit;
using MimeKit;
namespace TestClient {
class Program
{
public static void Main (string[] args)
{
var message = new MimeMessage ();
message.From.Add (new MailboxAddress ("", "test.user@mydomain.com"));
message.To.Add (new MailboxAddress ("", "test.recipient@anotherdomain.com"));
message.Subject = "Test message";
message.Body = new TextPart ("plain") { Text = "This is the message body." };
using (var client = new SmtpClient (new ProtocolLogger ("smtp.log"))) {
client.Connect ("smtp.office365.com", 587, SecureSocketOptions.StartTls);
client.Authenticate ("test.user@mydomain.com", "password");
client.Send (message);
client.Disconnect (true);
}
}
}
}
This will log the entire transaction to a file called "smtp.log" which you can then read through and see where things might be going wrong.
Note that smtp.log will likely contain an AUTH LOGIN command followed by a few commands that are base64 encoded (these are your user/pass), so if you share the log, be sure to scrub those lines.
I would expect this to have the same error as you are seeing with System.Net.Mail, but it will help you see what is going on.
Assuming it fails (and I expect it will), try changing to SecureSocketOptions.None and/or try commenting out the Authenticate().
See how that changes the error you are seeing.