If you're curious which protocols .NET supports, you can try HttpClient out on https://www.howsmyssl.com/
// set proxy if you need to
// WebRequest.DefaultWebProxy = new WebProxy("http://localhost:3128");
File.WriteAllText("howsmyssl-httpclient.html", new HttpClient().GetStringAsync("https://www.howsmyssl.com").Result);
// alternative using WebClient for older framework versions
// new WebClient().DownloadFile("https://www.howsmyssl.com/", "howsmyssl-webclient.html");
The result is damning:
Your client is using TLS 1.0, which is very old, possibly susceptible to the BEAST attack, and doesn't have the best cipher suites available on it. Additions like AES-GCM, and SHA256 to replace MD5-SHA-1 are unavailable to a TLS 1.0 client as well as many more modern cipher suites.
As Eddie explains above, you can enable better protocols manually:
System.Net.ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12 | SecurityProtocolType.Tls11;
I don't know why it uses bad protocols out-the-box. That seems a poor setup choice, tantamount to a major security bug (I bet plenty of applications don't change the default). How can we report it?