Why do amplifiers sound different?

Coming from a electrical engineering background,  amplifiers theoretically should all sound alike as when measured into an 8 ohm load,  their frequency response is extremely flat. 

Usually + or - less than 0.2 dB. Your ears can't detect that. 

What makes them sound different is the fact that speaker impedance various with frequency. All solid state amplifiers that do not have output transformers vary their output slightly depending on the impedance they see at each frequency. 

That's why matching amplifiers to speaker matters. 

All tube amplifiers have output transformers so they aren't affected by impedance fluctuations. 

That's one reason they sound better to most people. 

Odd vs even order harmonics is another but that's another discussion.