Why was this move a mistake?

The computer thinks that it's a mistake for black to play 20... Nxh4 here. Instead, the computer recommends that I should take this funny line as black:

My logic for taking with 20... Nxh4 was:

- Bishops are worth slightly more than knights in open positions like this

- When my opponent recaptures with his knight, he'll be on the edge of the board, and they say that "a knight on the rim is grim"

But it seems that my logic wasn't good enough... could someone please explain this to me?

The analysis thinks you stood to win a pawn.

Your move just led to a draw.

While your logic makes sense that bishops are worth a bit more in open positions.  You're missing whites obvious reply.  1...Nh4 2.Bh7+ and bye bye bishop pair.  Now you have a bishop vs. knight with pawns on both sides of the board, so you have the minor piece advantage. Whites queenside pawns are all on dark squares which limits your bishops mobility. 

The knight on the rim has a nice outpost on f5, and you traded off your LSB.  So how do you prevent the knight from planting itself on f5?  By playing the only move you have ...g6.  A move that does nothing but defend a weakness, while creating another weakness on f6.  And after white plays 2.Qg2 attacking the IQP, and adding pressure to blacks kingside, youre tying your queen down to defending a pawn. 

Why play 20...Rae8?  As the saying goes:  "Rooks belong on open files."  I would also argue that ether rook on e8 is fine too.  In fact i prefer 20...Rfe8  Why?  Count how many squares each rooks controls after placing either rook on e8.

I think a more advanced question is why is nf4 immediately inferior?  I haven't seen that question answered.  I believe I figured it out, and suggest that interested folks keep working it.  

to deranged in the "short" time your move is good yet it is considered a mistake because more important to attack opponents king than capture the bishop.

to notmtwain, your response about the pawn is balanced by the askers point that the bishop is more powerful meaning far reaching so stronger than the knight so pawn is not really a factor for benefit.

no way. not only would b not move h7 unprotected for the same reason of keeping a pair, but even if it would sacrifice BxB that would not define the knight as pinned nor moving it a "mistake error".