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
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!
There are at least three factors involved in how an amplifier sounds:

The engineering of the equipment (and its measurements).
The perceptual and psychological mechanisms involved (ear, brain).
The interpretative habits of the listener (habits, preferences -- taste).

What that says to me, at least, is that I can take with (more than) a grain of salt any claim beginning with "Coming from a electrical engineering background, amplifiers theoretically should all sound..."

The author of such a sentence simultaneously claims and disclaims their own expertise. This is the intellectual equivalent of stepping on a rake.
Hello vanson1. Question your assumptions. Not all tube amps have output transformers. Numbers given us by machines cannot tell a complete story to human beings. There are lots of women with 36-24-26 figures, same weight, same height; but are they all the same? Different capacitors with the same electrical specifications sound different. It's easy to demonstrate. Manufacturers of different amps use different parts. All 12AX7 tubes do not sound the same; ask any "tube roller." So . . . any assemblage of parts will have it's own "sound" due to the interaction of the signal it's handling with all the various parts. An iron wire has different characteristics than a copper wire or an aluminium one. If you are a beginner, a budding audiophile, you are entering a wonderful hobby which is mucher cheaper and safer that discovering the differences between all the ladies with simlar "specs."  A little experience will lead to a great deal of education, and a lot more questions. Enjoy the music1