SQL Cluster, AlwaysOn AG, or Something Else?
My Network Admin. wants an "Active/Active" with shared storage 


There is no such thing as an "active/active" instance.  Only one node of the cluster can be hosting the SQL instance for a failover cluster instance.  If by "active/active" you mean having two different SQL Server failover cluster instances, that is possible.

Why shared storage?  That's an odd "requirement", and usually comes as a need from a requirement, not typically a requirement itself.  The failover cluster instance would exercise shared storage, but different replicas in an availability group would have their own storage.


  load balancing


There is no load balancing with a failover cluster instance.  For an availability group, you can offload certain operations to secondary replicas (reporting/readonly workloads, backups, etc.), but there is no fully capable (data modifying) load that can be offloaded to a secondary.


  redundancy


This can be achieved with either a failover cluster instance and/or an availability group.


  auto-fail over


This can be achieved with either a failover cluster instance or an availability group.

One of the main questions you need to ask yourself is what level of high availability are you looking for?  A failover cluster instance will give you HA for the whole instance, whereas an availability group will give you high availability of a grouping of databases as a unit of failover.