I just "failed" this Lichess exercise. Main line is Stockfish's, secondary is mine's.

[FEN "r5k1/3N1p1p/2p1p1pb/3pP3/p2P3q/5P2/PP2QP1P/R4RK1 b - - 2 19"]

1...Bf4 2. Nf6 Kg7 {-5.4 according to Stockfish} (2...Kh8 {+1.9??} 3. Ng4 Qh3 {why not h5 already?} 4. Rf1d1 h5) 3. Ng4 h5 {Exercise completed successfully}

The basic idea was clearly to use the threat of a checkmate on h2 with the bishop and queen, and so I did.

The only option for white then was to check my king with the knight. After that, I figured it didn't really matter where my king escaped to (as long as it was safe), since white's next move would obviously be 3. Ng4 to protect h2 and prevent my mate attempt.

Some time ago I learned that "the safest spot to escape from a knight is two diagonal squares from it", since it'd take said knight at least three moves to get to a position where it can attack the same piece again.
So, to play it safe(r), I decided to go 2...Kh8 ...and that's where I failed!

But why? White's knight is going to g4 anyways and my pawn is going to h5 anyways, so what's the difference?