Classical players don't understand Hypermodern openings

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.

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.

Indeed indeed! Magnus Carlsen has shown recently that all that opening prep is of no use once you need to think outside of standard openings. Yet people who spend all day playing bullet with ratings around 300 will still lament the endless trickery of the Fried Liver and declare chess dead.

Is that a fact?!

When the OP talks about "Hypermodern Openings," he is describing opening ideas that were new and somewhat controversial in the 1920s! Every strong player today has grown up with a good understanding of both classical and hypermodern theory. The modern grandmaster is comfortable in the Nimzo-Indian or a Queens Gambit declined. It's all just part of chess to them

But still - I think the OP has a good idea - including if one is willing to go around the semantics pitfalls - even if the semantics in the opening post are controversial or questionable.
And the OP's opening post refers to 'novices'.
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Not 'strong players'.
I wouldn't be surprised if there are far over 100 forums here on the subject of the early approach to the openings - 
and if there turns out to be a common pattern too ...
where many strong players recommend 'deep' instead of 'wide'.
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And then display GM games or other master games.
But the novice is playing his/her own games.
It can be kept in mind that most players will never reach 2000 USCF nor its FIDE equivalent ... nor anywhere near those levels. Never do.
Some might say 'Never Premise that!'
but then a point is missed.
The aims of novice players.
Is it 'see what you can do? be all you can be?' Always?
Hint: every player is different.

Hint: every player is different.
Fact.

@206

"Chigorin liked knights too."
++ That is why he lost his match to Steinitz.
https://www.chessgames.com/perl/chessgame?gid=1036308

@205

"Nimzowitsch favored knights over bishops"
++ No, he valued the bishop's pair.
In this game he sacrificed a pawn with 11...O-O for the bishop's pair.
https://www.chessgames.com/perl/chessgame?gid=1272092

I was repeating Raymond Keene’s assertion in Aron Nimzowitsch: A Reappraisal, but also have noted the slight tendency to favor knights in my reading of My System and Blockade. He certainly espouses the superiority of the knight as a blockading piece.