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. 
vanson1
Coming from a electrical engineering background,

I’m sorry. Still, many audiophiles have much worse handicaps. (Not really, but trying to stay positive!) I recommend a complete memory wipe, followed by a month studying The Compete Guide to High End Audio by Robert Harley. With a lot more listening and a lot less engineering there may be hope for you yet.
"...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..."

What ever measurements we make, they really don't tell us how amplifiers sound. I can't tell you what measurements would tell us how amps sound but so far nobody knows what those measurements might be. 
Based on his posting history,  not worth my time to engage.  Have fun with it, team!

I'll say my usual: The greatest impediment to advancing an audio system is the audiophile.   :)
I disagree with the OP in total, but I guess it doesn't matter. He asked and answered his own question.
OP has a depth of understanding comparable to that of Julian Hirsch in 1970.  Since then a lot has arisen to pique the curiosity of both listeners and amp designers. The effect of global feedback was illustrated by Matti Ottala. Richard Marsh published his findings on capacitors. Bob Carver exposed how protection circuits can intrude on music reproduction. All applied to supposedly transparent SS amps with ruler flat response “from DC to light”. Today, we have D Class surging in the market with Hypex and Purifi. Long live the curious!