There are a lot of moves black can play in that position, so I wouldn't really worry about what the review says too much. However, after ...Nf6, Nxf6 you have ...Qxf6 which prevents your pawns from being doubled. Also, even if you did play ...gxf6 it wouldn't be the end of the world.
Why does analysis suggest to "Offer an equal trade of pieces"?

There are relatively few "equal" exchanges. One side or another usually gets something out of the deal. Perhaps you exchange one of your less active pieces for a well-placed piece of your opponents. Perhaps you can arrange to have a well-posted knight against a bishop blocked by its own pawns. These small differences add up

Doubled Pawns are not the end of the world anyway.
It is entirely possible for doubled Pawns to be an advantage instead of a disadvantage.
If you have doubled Pawns, then you also have a hybrid open file for your Rooks.
Doubled Pawns allow you to guard important squares that would otherwise be hard to defend. Example: Pawns on c3 and c4 allow you to defend both d4 and d5 with Pawns.

Also, that ISN'T an equal trade of pieces, and the engine is careless in describing it that way.
You are offering to trade a Knight that has moved ONCE (Ng8-f6) for a Knight that has moved THREE times (Nb1-c3-e4xf6). A Knight and one move vs a Knight and three moves. That is the trade being offered... and White loses two moves on that trade.
Also, that ISN'T an equal trade of pieces, and the engine is careless in describing it that way.
You are offering to trade a Knight that has moved ONCE (Ng8-f6) for a Knight that has moved THREE times (Nb1-c3-e4xf6). A Knight and one move vs a Knight and three moves. That is the trade being offered... and White loses two moves on that trade.
That's not really true. White would play 3 tempi with Nc3-e4-xf6 and black would have played d4, Nf6 and Qxf6. That is an equal exchange of tempi, the judgement on the merit of the trade comes from the quality of the pawn on d4 and the queen on f6. I would argue that the pawn being on d4 and the queen on f6 isn't really worth the tempi, therefore the trade is pretty much equal.

Also, that ISN'T an equal trade of pieces, and the engine is careless in describing it that way.
You are offering to trade a Knight that has moved ONCE (Ng8-f6) for a Knight that has moved THREE times (Nb1-c3-e4xf6). A Knight and one move vs a Knight and three moves. That is the trade being offered... and White loses two moves on that trade.
That's not really true. White would play 3 tempi with Nc3-e4-xf6 and black would have played d4, Nf6 and Qxf6. That is an equal exchange of tempi...
Pardon?
Also, that ISN'T an equal trade of pieces, and the engine is careless in describing it that way.
You are offering to trade a Knight that has moved ONCE (Ng8-f6) for a Knight that has moved THREE times (Nb1-c3-e4xf6). A Knight and one move vs a Knight and three moves. That is the trade being offered... and White loses two moves on that trade.
That's not really true. White would play 3 tempi with Nc3-e4-xf6 and black would have played d4, Nf6 and Qxf6. That is an equal exchange of tempi...
Pardon?
Putting your pieces on bad squares isn't gaining tempi. If white had really lost two tempi, black would have a significant plus. Black doesn't have a plus because the pawn on d4 and the queen on f6 aren't high quality and both will most likely have to "give back" the tempi because of the poor quality of their positioning.
If I moved a knight 20 times and then traded for a knight that never moved but it brings another piece to a bad square, allowing a winning tactic, then the side that lost did not gain 19 tempi from the trade.

Not sure I understand what's going to chase the Black Queen off of f6. The b1-Knight? It's gone. The c1-Bishop? It's blocked.
I will concede that we seem to have a very different way of looking at tempi, though.
Not sure I understand what's going to chase the Black Queen off of f6. The b1-Knight? It's gone. The c1-Bishop? It's blocked.
I will concede that we seem to have a very different way of looking at tempi, though.
If the trade is not equal, then prove how black gains anything. Did white give up a significant plus or did black gain one? If so, then how? If not, then its equal. The c1 bishop won't always be blocked and the queen might find the need to move of its own volition simply because it's on a bad square, not doing anything but defending pawns. The pawn on d4 is under attack and will likely get traded off.

In the image below, the engine suggests knight to f6, with the reasoning "This offers an equal trade of pieces.". I'm not questioning whether this might be the best move in the long run, but specifically the reasoning.
The reasoning has nothing to do with the engine.
It's a chess.com script that writes these things, and it's really bad. Just ignoring it is best. Don't use "Game review", use "Analysis" instead.

And yet you still peddle incorrect dogmatic ideas and pretend that you're an authority.
Nice edit though. Let it be known that I wasn't the first one to start slinging insults.
In the interest of amity I have removed the offending remark, but left an edit to show it used to exist. My bad.
That's as far as I'll go towards the halfway point, though. Your views on tempi are nonsense.
White will probably someday decide to move his Queen again, at some point, so you claim the Queen move represents a loss of tempi? Seriously? Doesn't this overlook the diminishing value of a single tempo, as more and more pieces come out? By the time development is complete, the phrase "loss of tempo" no longer means the same thing as it did in the early opening.
And yet you still peddle incorrect dogmatic ideas and pretend that you're an authority.
Nice edit though. Let it be known that I wasn't the first one to start slinging insults.
In the interest of amity I have removed the offending remark, but left an edit to show it used to exist. My bad.
That's as far as I'll go towards the halfway point, though. Your views on tempi are nonsense.
White will probably someday decide to move his Queen again, at some point, so you claim the Queen move represents a loss of tempi? Seriously? Doesn't this overlook the diminishing value of a single tempo, as more and more pieces come out? By the time development is complete, the phrase "loss of tempo" no longer means the same thing as it did in the early opening.
No, there is no loss of tempo, there is just no gain because there was nothing gained. There is a slight benefit to the queen being on f6, in that the queen is off the back rank which means the rooks can coordinate a move sooner. But that queen on f6 is likely to be vulnerable to attack at some point while it is doing next to nothing. The pawn on d4 is probably going to help white open the e-file and if black initiates the trade of that pawn, white will have a central majority and/or regain the tempi depending on how they recapture. Not game losing but the overall net gain, in my evaluation, is next to zero which makes the trade equal. Let us not forget that your original claim is that the trade was not equal. The overarching point is that to gain a tempo in my eyes, means you must be gaining something for that time. Having more visible moves made on the board is completely meaningless if those moves aren't useful.
In the image below, the engine suggests knight to f6, with the reasoning "This offers an equal trade of pieces.". I'm not questioning whether this might be the best move in the long run, but specifically the reasoning. If white trades, I'll have double pawns on f, which the engine consistently suggests against.