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Why trading this knight is a mistake?

No, if you traded knights then your opponentcould have taken with the g pawn and get a half open file in front of the king to attack in.
Wow thank you all for your great insights, I just thought to eliminate black's only active piece but it actually made room for other black pieces come into play.
@ngducphu

Ne4 is using the holes in this structure and is a lot stronger. Also Knight on e4 often is a beast, even in some open games. Trading knights only helps black to control more squares and get away his knight with not so much potential as yours.
There is no general rule. Sometimes it is good to take, sometimes not. In this case you would only help black.
The most natural move here is Ne4. One point is to kick off the knight on f5 with g4, but of course it does not work if black plays h5. But the more important part is that the Ne4 has an eye on c5. If Black cannot push c5 his light squared bishop is really bad. He has to play c5 or f6 sometime. And the knight on e4 is obeying both squares.
Speaking of "great insights," OP...didn't the engine give you any alternative lines to the knight capture?
The engine gave g4 which I think weakens the kings but in hindsight, the black king is actually much weaker.
Sometimes I consider a strong move then write it off for some weird reasons, then just play a worse move instead.

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