What are the benefits of using Manual Failover Mode in an AlwaysOn Availability Group instance as opposed to Automatic Failover Mode? Why wouldn't I want to use Automatic Failover as the Failover Mode for an AlwaysOn Availabiltiy Group instance?

Are there pros for Manual Failover Mode that don't exist for Automatic Failover Mode?
If you have synchronous replicas you typically have one with automatic failover.  The most common reason not to is when the primary is hosted on a Failover Cluster Instance, and it's a rule that only the FCI can failover automatically in that configuration.

But you could also have a scenario where you would prefer an outage over a failover, for instance if the secondary replica is not accessible from the application.