The current implementation of HttpWebRequest in .Net 4.6 lacks RemoteCertificateValidationCallback similar to that of SslStream class. This makes mutual authentication impossible, especially when client becomes aware of mutual authentication enforced by server only after SSL handshake has been initiated.
Currently all certificate callbacks for HttpWebRequest is managed by ServicePointManager class, I request to include this feature in corefx releases.
Please see this question in SO.