Why will a switch never learn a broadcast address?

Switch is working under layer 2. So it will not use any broadcast instead of that it will use mac address.

a broadcast address is not a source address, it's only a destination.

Switches learns the MAC addresses of its hosts to update MAC Database (CAM Table). MAC Addresses with all the F's on are broadcast addresses which broadcast into 1 broadcast domain and will be learn by each host in same broadcast domain. Broadcast addresses are used to find the destination host connected to switch because switch don't have the MAC Address of destination host. e.g., Host A sends frame to Host B but switch don't have MAC address of Host B so switch will broadcast to each host except Source port from where it received the frame. Host B will reply that broadcast and all other hosts will discard that frame. I hope you are cleared now that why & how switch broadcast?

Switch work in layer 2(Data link layer) ,  and work with mac address 

but broadcast is an ip  and it in layer 3 (Network layer)

A broadcast address ffff.ffff.ffff.ffff is meant for all as destinations. And it is not a host MAC address. So the switch will always a MAC table for the connected hosts not the broadcast address.

Switches learn address from the source of the frame

Switch will learn only source mac address, and broadcast will never be in source mac

A broadcast address will never be the source address of a frame

because ffff.ffff.ffff is a broadcast address .means go and find out this address (it is a instruction for switch) but eventually this address we can not assign to any device , switch is not able to find out this address so thats the only reason ,switch never learn this address.