What is one of the advantages of using both symmetric and asymmetric cryptography in SSL/TLS?

Symmetric algorithms such as AES provide a failsafe when asymmetric methods fail.

Asymmetric cryptography is computationally expensive in comparison. However, it is well-suited to securely negotiate keys for use with symmetric cryptography.

Symmetric encryption allows the server to securely transmit the session keys out-of-band.

Supporting both types of algorithms allows less-powerful devices such as mobile phones to use symmetric encryption instead.