My understanding is that valves sound better because the 2nd harmonic distortion sounds better.
No, I do not understand audiophools' reasoning.
That is true. Vacuum tubes generate even order harmonics which supposedly sound "smooth". Transistors generate odd order harmonics which supposedly sound "harsh".
But I truly believe you need the hearing of Fido in order to tell the difference but many phools claim they can.
[SOAPBOX MODE] 
Sorry... musicians can tell the difference; so there
has to be something. As it is generally
their preference upon which the source material is built,
I'm sure that some... ahem... critical listeners can tell the difference, just as you and I can tell the difference between a square wave and a sine wave played through a loudspeaker.Consider this: the tinkerdwagon's big snout isn't all for show; I (and my son) were blessed with unusual olfactory acuity for human beings. As in, I used to be able to track animals by scent, and I knew my farm animals from those belonging to other farms. Flop sweat (even minute, invisible amounts) is particularly acrid, and it makes my hackles rise when I smell it, as I know someone is peddling bullshit in my vicinity. Also "grrl fumes" (as I refer to that group of pheromones that a strong-willed female emanates)...
*si-i-i-igh* ...they literally make me feel euphoric.

Point being... some people have an unusual acuity in one or more senses; it alters your entire outlook on reality, and how you interact with the world around you. And for me, part of that is teaching my son how to use that olfactory acuity to give him an edge dealing with the world, and how
not to be a slave to it, as many are.
We have no problem accepting that a sniper has exceptional visual acuity, or that a surgeon has exceptional sense of touch/dexterity; yet somehow the notion that someone can
hear exceptionally well and can hear things we cannot seems to be something we hold a particular prejudice against, the same way stupid people take offense at being called stupid.

Now yes, I get that
some of the audio-phoolery we loathe is just
wishing they had hearing acuity similar to that of the people who made the music they love, combined with a certain amount of confirmation bias. For we who are all about measurable, quantifiable signal quality, much if not all of the "awesome sauce" bandied about in these circles does seem like yet
another aspect of the usual
"My, what a gullible breed..." syndrome.
But arguing that one particular brand of tube cannot have a different "sound" from another, when they are actually physically constructed differently because each company's engineers had a different vision for how best to make a particular classification of valve... I can't say I agree with that.Just because the diagram for how they're constructed looks the same does not mean they function exactly the same;
things like exact spacing/shape of the elements of the tube have to affect how it amplifies/mixes/distorts the sound, for the same reason we have thousands of different types of silicon transistors, each one optimized for a certain purpose, yet they all have the same symbol.
Honestly, between the shameless vitriolic loathing of everything we can shove in the "audiophoolery" pigeonhole, and the way we seem to feel that our use for tubes is the
only important one,
we tend to be pretty fucking judgemental and even prejudiced in here.Of course it makes me cringe when I see/hear of someone trashing a perfectly good (or even marginally good in need of TLC) hollow-state scope or counter, etc just to get to those big-$$$ choobs...
but it is the trashing of the device I loathe, not the harvesting of valves. As far as I'm concerned,
if someone pulls the tubes out of such a device carefully and non-destructively, that is in and of itself showing the respect it is due, and those tubes are a consumable supply anyways.
We who enjoy hollow-state need to separate "but the choob-vultures made fixing this particular one so fucking expensive" aggravation from that where actual sins are committed in the acquisition of said choobs.If the only real gripe we can honestly lay at someone's feet is that their hobby makes our hobby more expensive, then we are ourselves guilty of some pretty severe prejudice, compounded with the very blend of confirmation bias and Dunning-Kruger we habitually accuse the audiophools of; only it is literally the inverse function, the flip side of that same coin. [/SOAPBOX MODE]mnem
We knew that this was a expensive hobby when we got into it. Hating others for that fact is just dumb.