Classical players don't understand Hypermodern openings

I think Tarrasch was considered to have been the stronger by contemporary players. Nimzo is thought to have contributed more but that's due to the importance of the NimzoIndian Defence. Tarrasch and another one, Schlechter, were immensely important. In my opinion, much more so than Emanuel Lasker. Two generations before, perhaps along with Staunton, Louis Paulsen deserves to be recognised as the father or progenitor of modern chess..

Black should play ...Nd7 on autopilot whenever White threatens to bring a knight to e5. This way, Black can play ...Nxe5 if the White knight ever tries to invade Black's camp.

Interestingly, most Americans use "could care less", which originated as a kind of irony. I think I know who you are. I've thought so for ages though but we're getting closer. However, you've revealed something which was a mystery to me. I had no idea that facts are facts.

I play the Caro-Kann a little, although I know it much less well than the Paulsen Sicilians. However, 6. ...h6 is very weakening and I think 6. e6 is correct.

Yes - but do you see Ziryab's post which I will copy below -

"Ziryab #192
e6 is the normal move against Nf3
Adopting the second most popular line in the opening is often a useful way to provoke small errors. As these add up, a larger error sometimes occurs in the face of pressure."
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Its a good thing Black has at least e6 as viable there - without an option there the Caro would be out of business.
Plus regarding the 'business' of bishop development in the openings (in my humble opinion - the most critical issue of openings)
the issues of bishops developing to squares like f4 and f5 - well every now and then the other side will swing a knight to h4 (or h5 if its black) attacking that bishop - and even if its not much in books an opponent is likely to try it out and the other player has to deal with it.
In the line shown in Ziryab's game - it appears that white can get rid of black's bishop with his knight plus double black's gpawn but many might say 'so what? White invested three knight moves to do that plus parted with his valuable g-knight plus black has a half-open h-file with his rook there and no isolani.'

Losing the B isn't a problem for black, who shouldn't want to use two moves to keep it on the board and weaken the king-side into the bargain. You chop off a knight if it lands on your king-four square if you must or if it weakens the opposition to do so. Otherwise drive it away with the f-pawn.

Since white has options of both Ne5 and Nh4 - black can't prevent both of those attacks on his bishop after Nf3 ... He prevents Nh4 with e6. He can alternatively counter or deter Ne5 with Nd7. But he does not have a move to counter both of them.
Black's already moved his bishop twice - while white has moved his b-knight 3 times and will need to move his f-knight three times to get rid of black's bishop.
That's six knight moves. Black should worry about his two bishop moves?
No.

Agreed - Black shouldn't worry about a knight for bishop trade there.

Besides - that's Black's bad bishop, anyway. If White is determined to exchange, Black can say, "Thanks, White, for removing my problem piece. You're too kind."

Agreed.
I can see a Sicilian coach arguing though ...
'Just look what happened to your c-bishop in that Caro Kann line there! Do you want that? In the Sicilian you'll get to keep your two bishops and gradually turn the tide in the center and your two bishops will Wreak Havoc on white. Forget the Caro!'
Which has some validity. Black might really get that in the Sicilian some of the time.
But the Caro-Kann is very much in business.
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Is there a paradox?
There are many in chess including in openings.
The coach might do better to say something like 'avoid dogmatism in openings. Don't fill your mind with syllogisms about 'two bishops'. .'
There are many ways to guide your play.
But a lot of the game is about figuring out good moves for the situation in front of you. If you're having to evaluate by 'go to's'' instead ... uh oh ...
there goes the learning curve ...

Most if not all of us here have probably heard:
'Don't move a piece twice in the opening.'
'Don't move your queen early.'
'Don't make a lot of pawn moves in the opening'
'Knights before bishops'
'Put pawns in the center'
and so on.
But experienced players (and coaches) know that all these 'rules' are broken constantly including in good play.

In my teens, I was coached by an NM who favored knights over bishops - and he showed me many high-level games where knights proved to be the most valuable pieces on the board ...

So these days, I don't worry too much about the bishop pair. Sometimes it matters. Sometimes it doesn't at all.

As he liked to (half-jokingly) say, "Now we're of course going to win, because we have the knight pair!"

"So these days, I don't worry too much about the bishop pair. Sometimes it matters. Sometimes it doesn't at all."
At your 2391 level - looks like your NM coach has and had the beneficial objectivity about knights and bishops.
Much more critical than 'the two bishops' in openings is 'bishop placement'.
A much better idea to work with. Your bishops. Your opponent's bishops.
In my humble opinion - bishop placement is the most critical issue in openings.

Nimzowitsch favored knights over bishops

Chigorin liked knights too.
A bishop covers only 32 squares to a knight's 64.
I like to think of that as a fact rather than as a generalization.

It's a generalisation, since the scope of each piece depends on the board position. It therefore obviously isn't a fact.

Stands. (although somebody doesn't seem to realize that facts and generalizations aren't exclusive of each other. Has he been imagining all these decades that they're digital A or B? Not I.)
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Because regardless of the position a bishop can still only move on 32 squares maximum.
Whereas a knight can have up to 64 squares available.
A fact of the rules of chess.
But whoever - could quibble about the semantics of what a fact is.
And keep forgetting about facts too.
Also obvious - a fact can be a generalization but doesn't have to be.
A generalization can be a fact - but also doesn't have to be. Could be in error.
A knight can cover up to 64 squares.
Fact.
So now I'll qualify it.
I like to think its fact. And it is. Obviously.
Its also a generalization - but an accurate one.
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Getting back to the forum subjects - 
Strong players have now affirmed that 'the two bishops' can be overrated ...
to 'get into' the subject of 'hypermodern' openings ...
knights and bishops and exchanges of one for the other is clearly relevant.
Experienced players know that bishops and knights constantly exchange roles as 'Cat and Mouse' ...
including in the Caro Kann main line being discussed.
Bf5 attacking the knight and the reply Ng3 immediately returning the attack 'favor'.
Point: the dogmatism of 'two bishops'.
Seems to enter into discussions of coaching in the opening.

This all has been derailed long ago. The OP set up a ridiculous set of generalizations about what's keeping people from improving that dragged in a bogus division between "classical players" and needing to read "My System" to understand hypermodern play. Since then it has gone off into arguments about specific openings that really don't help anyone understand anything about hypermodern chess or even the openings discussed. Given that and the nature of people to argue about nonsense for ages, this will likely go on for a couple more months for dozens of more pages.

"set up a ridiculous set of generalizations"
but by being provocative - the OP got response.
The generalizations were subject to a lot of semantics variations ...
But regarding 'failure to improve' (even with coaching)
the study of how those gremlins get in there and flatten the learning curve ... well that happens.
In any field of endeavor - eventually whoever runs into a wall that can't be surmounted.
Usually.
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Most chess novices aren't going to get past 1600 USCF.
Very few reach 2000.
With various obstacles removed early - a lot more might reach 2000 ... but again they'd run into a wall there. Instead of 1600.
That jump to Master at 2200 is very elusive.
Which is probably the origin of how that Title evolved ...
A level was chosen that even with a lot of intelligence and dedication and good training including early in life - few would get there.
Same thing with major league baseball.
Or 'making the cut' in golf PGA tour Open events.
So few can do it.

Indeed. It is one of the most interesting threads I’ve seen in a while. Was a time when most of the chess discussion in these forums wasn’t beginners looking for that magic opening to get over 900.