With White to play, I have trouble understanding what goes on in this puzzle. First of all, how exactly Kh1 is preferable to Kxh2? I know that Black can give checks after Kxh2, but there really is no mate threat anyway and White gets rid of a pawn that way. Also, why does Black follow up with Qe3, which leads to them losing a piece? Is there not a better move for them to play?
[fen "1r5k/1p5p/p5p1/2P1rRq1/P2Q4/8/1P5p/5RK1 w - - 0 2"] 1. Kh1 Qe3 2. Qxe5 Qxe5 3. Rxe5