Black has an obvious material advantage. Black goal is to win. To win, he must queen a pawn. Black’s chances go down considerably if white captures the f-pawn since white is in a good position to stalemate with his king in the corner.
White’s king is well positioned to defend, White’s goal is to draw. To do so, he almost certainly needs to capture the f-pawn and then strive for a stalemate position.
Move 1 for White
White must stop the pawn from queening and so 1. Kg2 is the only viable move.
Move 1 for Black
Kd3, Kd4, Kd5, Ke5, or Kf5 don’t make any progress regarding black’s objective to queen a pawn; black loses time and gets no compensation for the the loss of the f-pawn.
1. … Kf4 3. Kxf2 and white will be able to reach either g1 or g2 to secure the draw
1. … h3 attempts to distract white’s king but white simply responds with 3. Kxf2
1. … f1Q+ 3. Kxf1 is pointless since white can reach the critical square g1 to draw the position
1. … Ke3 is the only move remaining and the only move that saves the f-pawn.
Move 2 for White
2. Kh2?? is tricky since 2. … f8Q?? is stalemate. However, we don’t make moves to trick our opponents. We strive to play good chess. If this position is lost, then this position is lost.
Anyways, white has a chance to draw here. No reason to make a move that just loses!
The only move that keeps white in the game is 2. Kf1, blocking the pawn and covering the e2 square.
Move 2 for Black
2. … Kf3 and 2. … h3 both stalemate. Black tries to make forward progress with 2. … Kf4.
And now 3. Kxf2 h3 4. Kg1 Kg3 5. Kh1 and the position is drawn.