Ryan Adams discovered that Database Mail cannot use TLS 1.2 at this time:
You may recall something called the POODLE attack that revealed a vulnerability in SSL 3.0 and TLS 1.0. This particular server had SSL 3.0, TLS 1.0, and TLS 1.1 disabled in the registry. Also note that TLS 1.2 was NOT disabled. The server was running Windows 2012 R2. These protocols were disabled to prevent the possibility of a POODLE attack. If you are wondering how to disable these protocols on your servers then look at Microsoft Security Advisory 3009008. To disable them for the whole OS scroll down to the Suggested Actions section and look under the heading “Disable SSL 3.0 in Windows For Server Software”.
I also want to note that the PCI Security Standards Council pushed back the date for getting off of SSL and TLS 1.0 to June 30th, 2018. In addition to that, it should also be noted that Microsoft’s Schannel implementation of TLS 1.0 is patched against all known vulnerabilities.
The root cause is interesting: it’s because Database Mail requires .NET Framework 3.5. Ryan has more details, including a fix, so read on.